--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/00README.XXX	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,1 @@
+nohypertex

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ant-arxiv.bat	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,1 @@
+ant arxiv

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ant-arxiv.sh	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,1 @@
+ant arxiv

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ant-eps-diagrams.bat	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,1 @@
+ant eps-diagrams

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ant-pdf.bat	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,1 @@
+ant pdf

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ant-pdf.sh	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,1 @@
+ant pdf

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/bibliography/bibliography.bib	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,405 @@
+@PREAMBLE{ "\newcommand{\noopsort}[1]{}" }
+
+@STRING{CUP = {Cambridge University Press}}
+@STRING{OUP = {Oxford University Press}}
+@STRING{PUP = {Princeton University Press}}
+@STRING{SV = {Springer-Verlag}}
+@STRING{AP = {Academic Press}}
+@STRING{AMS = {American Mathematical Society}}
+
+@article {MR1917056,
+    AUTHOR = {Bar-Natan, Dror},
+     TITLE = {On {K}hovanov's categorification of the {J}ones polynomial},
+   JOURNAL = {Algebr. Geom. Topol.},
+  FJOURNAL = {Algebraic \& Geometric Topology},
+    VOLUME = {2},
+      YEAR = {2002},
+     PAGES = {337--370 (electronic)},
+      ISSN = {1472-2747},
+   MRCLASS = {57M27},
+  MRNUMBER = {MR1917056 (2003h:57014)},
+MRREVIEWER = {Jacob Andrew Rasmussen},
+      note = {arXiv:\arxiv{math.QA/0201043}},
+}
+
+@incollection {MR2147420,
+    AUTHOR = {Bar-Natan, Dror},
+     TITLE = {Khovanov homology for knots and links with up to 11 crossings},
+ BOOKTITLE = {Advances in topological quantum field theory},
+    SERIES = {NATO Sci. Ser. II Math. Phys. Chem.},
+    VOLUME = {179},
+     PAGES = {167--241},
+ PUBLISHER = {Kluwer Acad. Publ.},
+   ADDRESS = {Dordrecht},
+      YEAR = {2004},
+   MRCLASS = {57M27},
+  MRNUMBER = {MR2147420 (2006c:57009)},
+MRREVIEWER = {Marta M. Asaeda},
+}
+
+@article {MR2174270,
+    AUTHOR = {Bar-Natan, Dror},
+     TITLE = {Khovanov's homology for tangles and cobordisms},
+   JOURNAL = {Geom. Topol.},
+  FJOURNAL = {Geometry and Topology},
+    VOLUME = {9},
+      YEAR = {2005},
+     PAGES = {1443--1499 (electronic)},
+      ISSN = {1465-3060},
+   MRCLASS = {57M27 (57M25)},
+  MRNUMBER = {MR2174270},
+      note = {arXiv:\arxiv{math.GT/0410495}},
+}
+
+@article {MR1680395,
+    AUTHOR = {Khovanov, Mikhail and Kuperberg, Greg},
+     TITLE = {Web bases for {${\rm sl}(3)$} are not dual canonical},
+   JOURNAL = {Pacific J. Math.},
+  FJOURNAL = {Pacific Journal of Mathematics},
+    VOLUME = {188},
+      YEAR = {1999},
+    NUMBER = {1},
+     PAGES = {129--153},
+      ISSN = {0030-8730},
+     CODEN = {PJMAAI},
+   MRCLASS = {17B37 (22E60 57M27 81R05)},
+  MRNUMBER = {MR1680395 (2000j:17023a)},
+MRREVIEWER = {Robert J. Marsh},
+      note = {arXiv:\arxiv{q-alg/9712046}},
+}
+
+@article {MR1740682,
+    AUTHOR = {Khovanov, Mikhail},
+     TITLE = {A categorification of the {J}ones polynomial},
+   JOURNAL = {Duke Math. J.},
+  FJOURNAL = {Duke Mathematical Journal},
+    VOLUME = {101},
+      YEAR = {2000},
+    NUMBER = {3},
+     PAGES = {359--426},
+      ISSN = {0012-7094},
+     CODEN = {DUMJAO},
+   MRCLASS = {57M27 (57R56)},
+  MRNUMBER = {MR1740682 (2002j:57025)},
+}
+
+@article {MR1928174,
+    AUTHOR = {Khovanov, Mikhail},
+     TITLE = {A functor-valued invariant of tangles},
+   JOURNAL = {Algebr. Geom. Topol.},
+  FJOURNAL = {Algebraic \& Geometric Topology},
+    VOLUME = {2},
+      YEAR = {2002},
+     PAGES = {665--741 (electronic)},
+      ISSN = {1472-2747},
+   MRCLASS = {57M27 (57R56)},
+  MRNUMBER = {MR1928174 (2004d:57016)},
+MRREVIEWER = {Jacob Andrew Rasmussen},
+    note   = {arXiv:\arxiv{math.GT/0103190}},
+}
+
+@article {MR2034399,
+    AUTHOR = {Khovanov, Mikhail},
+     TITLE = {Patterns in knot cohomology. {I}},
+   JOURNAL = {Experiment. Math.},
+  FJOURNAL = {Experimental Mathematics},
+    VOLUME = {12},
+      YEAR = {2003},
+    NUMBER = {3},
+     PAGES = {365--374},
+      ISSN = {1058-6458},
+   MRCLASS = {57M27 (18G60 57M25 57R56)},
+  MRNUMBER = {MR2034399 (2004m:57022)},
+MRREVIEWER = {Jacob Andrew Rasmussen},
+}
+
+@article {MR2100691,
+    AUTHOR = {Khovanov, Mikhail},
+     TITLE = {sl(3) link homology},
+   JOURNAL = {Algebr. Geom. Topol.},
+  FJOURNAL = {Algebraic \& Geometric Topology},
+    VOLUME = {4},
+      YEAR = {2004},
+     PAGES = {1045--1081 (electronic)},
+      ISSN = {1472-2747},
+   MRCLASS = {57M27 (18G60 57R56)},
+  MRNUMBER = {MR2100691 (2005g:57032)},
+MRREVIEWER = {Justin Sawon},
+      note = {arXiv:\arxiv{math.QA/0304375}},
+}
+
+@article {MR2124557,
+    AUTHOR = {Khovanov, Mikhail},
+     TITLE = {Categorifications of the colored {J}ones polynomial},
+   JOURNAL = {J. Knot Theory Ramifications},
+  FJOURNAL = {Journal of Knot Theory and its Ramifications},
+    VOLUME = {14},
+      YEAR = {2005},
+    NUMBER = {1},
+     PAGES = {111--130},
+      ISSN = {0218-2165},
+   MRCLASS = {57M27},
+  MRNUMBER = {MR2124557 (2006a:57016)},
+MRREVIEWER = {Marta M. Asaeda},
+}
+
+@article {MR2171235,
+    AUTHOR = {Khovanov, Mikhail},
+     TITLE = {An invariant of tangle cobordisms},
+   JOURNAL = {Trans. Amer. Math. Soc.},
+  FJOURNAL = {Transactions of the American Mathematical Society},
+    VOLUME = {358},
+      YEAR = {2006},
+    NUMBER = {1},
+     PAGES = {315--327 (electronic)},
+      ISSN = {0002-9947},
+     CODEN = {TAMTAM},
+   MRCLASS = {57Q45},
+  MRNUMBER = {MR2171235},
+      note = {arXiv:\arxiv{math.GT/0207264}},
+}
+
+@misc{math.QA/0401268,
+    title = {{Matrix factorizations and link homology}},
+    author = {Mikhail Khovanov and Lev Rozansky},
+      note = {arXiv:\arxiv{math.QA/0401268}}}
+
+@misc{math.QA/0505056,
+    title = {{Matrix factorizations and link homology II}},
+    author = {Mikhail Khovanov and Lev Rozansky},
+      note = {arXiv:\arxiv{math.QA/0505056}}}
+
+@incollection {MR2048108,
+    AUTHOR = {Thurston, Dylan P.},
+     TITLE = {The algebra of knotted trivalent graphs and {T}uraev's shadow
+              world},
+ BOOKTITLE = {Invariants of knots and 3-manifolds (Kyoto, 2001)},
+    SERIES = {Geom. Topol. Monogr.},
+    VOLUME = {4},
+     PAGES = {337--362 (electronic)},
+ PUBLISHER = {Geom. Topol. Publ., Coventry},
+      YEAR = {2002},
+   MRCLASS = {57M25 (57M15 57M20 57Q40)},
+  MRNUMBER = {MR2048108 (2005c:57010)},
+MRREVIEWER = {Marko Kranjc},
+      note = {arXiv:\arxiv{math.GT/0311458}},
+}
+
+@article {MR1403861,
+    AUTHOR = {Kuperberg, Greg},
+     TITLE = {Spiders for rank {$2$} {L}ie algebras},
+   JOURNAL = {Comm. Math. Phys.},
+  FJOURNAL = {Communications in Mathematical Physics},
+    VOLUME = {180},
+      YEAR = {1996},
+    NUMBER = {1},
+     PAGES = {109--151},
+      ISSN = {0010-3616},
+     CODEN = {CMPHAY},
+   MRCLASS = {17B10 (22E60 81R05)},
+  MRNUMBER = {MR1403861 (97f:17005)},
+MRREVIEWER = {Stefano Capparelli},
+      note = {arXiv:\arxiv{q-alg/9712003}},
+}
+
+@misc{math.GT/0606318,
+    title  = {{Fast Khovanov Homology Computations}},
+    author = {Dror Bar-Natan},
+    note   = {arXiv:\arxiv{math.GT/0606318}},
+    url    = {http://www.math.toronto.edu/~drorbn/papers/FastKh/}
+    }
+
+@misc{math.GT/0603347,
+    title = {{On the Algebraic Structure of Bar-Natan's Universal
+        Geometric Complex and the Geometric Structure of Khovanov
+        Link Homology Theories}},
+    author = {Gad Naot},
+    note   = {arXiv:\arxiv{math.GT/0603347}}}
+
+@misc{math.QA/9909027,
+    title = {{Planar algebras, I}},
+    author = {Vaughan F. R. Jones},
+    note   = {arXiv:\arxiv{math.QA/9909027}}}
+
+@article {MR1217386,
+    AUTHOR = {Turaev, V. and Wenzl, H.},
+     TITLE = {Quantum invariants of {$3$}-manifolds associated with
+              classical simple {L}ie algebras},
+   JOURNAL = {Internat. J. Math.},
+  FJOURNAL = {International Journal of Mathematics},
+    VOLUME = {4},
+      YEAR = {1993},
+    NUMBER = {2},
+     PAGES = {323--358},
+      ISSN = {0129-167X},
+   MRCLASS = {57M25 (17B37 57N10)},
+  MRNUMBER = {MR1217386 (94i:57019)},
+MRREVIEWER = {Toshitake Kohno},
+}
+
+@article {MR1470857,
+    AUTHOR = {Wenzl, Hans},
+     TITLE = {{$C\sp *$} tensor categories from quantum groups},
+   JOURNAL = {J. Amer. Math. Soc.},
+  FJOURNAL = {Journal of the American Mathematical Society},
+    VOLUME = {11},
+      YEAR = {1998},
+    NUMBER = {2},
+     PAGES = {261--282},
+      ISSN = {0894-0347},
+   MRCLASS = {46L89 (17B37 46L05)},
+  MRNUMBER = {MR1470857 (98k:46123)},
+MRREVIEWER = {Andrzej Sitarz},
+    eprint = {\url{http://ftp.ams.org/jams/1998-11-02/S0894-0347-98-00253-7/S0894-0347-98-00253-7.pdf}},
+}
+
+@misc{math.GT/0603307,
+    title  = {{The universal sl3-link homology}},
+    author = {Marco Mackaay and Pedro Vaz},
+    note  = {arXiv:\arxiv{math.GT/0603307}}}
+
+ @misc{wiki:Grothendieck-group,
+   author = "Wikipedia",
+   title = "Grothendieck group --- Wikipedia{,} The Free Encyclopedia",
+   year = "2006",
+   note = "[\href{http://en.wikipedia.org/w/index.php?title=Grothendieck_group&oldid=52451663}{Online}; accessed 30-June-2006]"
+ }
+
+ @misc{wiki:Invariant-basis-number,
+   author = "Wikipedia",
+   title = "Invariant basis number --- Wikipedia{,} The Free Encyclopedia",
+   year = "2006",
+   note = "[\href{http://en.wikipedia.org/w/index.php?title=Invariant_basis_number&oldid=85220456}{Online}; accessed 24-December-2006]"
+ }
+
+@article {MR1403351,
+    AUTHOR = {Etingof, Pavel and Kazhdan, David},
+     TITLE = {Quantization of {L}ie bialgebras. {I}},
+   JOURNAL = {Selecta Math. (N.S.)},
+  FJOURNAL = {Selecta Mathematica. New Series},
+    VOLUME = {2},
+      YEAR = {1996},
+    NUMBER = {1},
+     PAGES = {1--41},
+      ISSN = {1022-1824},
+     CODEN = {SMATF6},
+   MRCLASS = {17B37 (16W30 18D20 81R50)},
+  MRNUMBER = {MR1403351 (97f:17014)},
+MRREVIEWER = {Yu. N. Bespalov},
+}
+
+@article {MR1669953,
+    AUTHOR = {Etingof, Pavel and Kazhdan, David},
+     TITLE = {Quantization of {L}ie bialgebras. {II}},
+   JOURNAL = {Selecta Math. (N.S.)},
+  FJOURNAL = {Selecta Mathematica. New Series},
+    VOLUME = {4},
+      YEAR = {1998},
+    NUMBER = {2},
+     PAGES = {213--231, 233--269},
+      ISSN = {1022-1824},
+     CODEN = {SMATF6},
+   MRCLASS = {17B62 (16W35 17B37 18D20)},
+  MRNUMBER = {MR1669953 (2000i:17033)},
+MRREVIEWER = {Benjamin David Enriquez},
+      note = {arXiv:\arxiv{q-alg/9701038}},
+}
+
+@article {MR1771217,
+    AUTHOR = {Etingof, Pavel and Kazhdan, David},
+     TITLE = {Quantization of {L}ie bialgebras. {IV}. {T}he coinvariant
+              construction and the quantum {KZ} equations},
+   JOURNAL = {Selecta Math. (N.S.)},
+  FJOURNAL = {Selecta Mathematica. New Series},
+    VOLUME = {6},
+      YEAR = {2000},
+    NUMBER = {1},
+     PAGES = {79--104},
+      ISSN = {1022-1824},
+     CODEN = {SMATF6},
+   MRCLASS = {17B37 (32G34 81R50)},
+  MRNUMBER = {MR1771217 (2002i:17021)},
+}
+
+@article {MR1771218,
+    AUTHOR = {Etingof, Pavel and Kazhdan, David},
+     TITLE = {Quantization of {L}ie bialgebras. {V}. {Q}uantum vertex
+              operator algebras},
+   JOURNAL = {Selecta Math. (N.S.)},
+  FJOURNAL = {Selecta Mathematica. New Series},
+    VOLUME = {6},
+      YEAR = {2000},
+    NUMBER = {1},
+     PAGES = {105--130},
+      ISSN = {1022-1824},
+     CODEN = {SMATF6},
+   MRCLASS = {17B37 (17B69 81R50)},
+  MRNUMBER = {MR1771218 (2002i:17022)},
+}
+
+@article {MR2253455,
+    AUTHOR = {Bar-Natan, Dror and Morrison, Scott},
+     TITLE = {The {K}aroubi envelope and {L}ee's degeneration of {K}hovanov
+              homology},
+   JOURNAL = {Algebr. Geom. Topol.},
+  FJOURNAL = {Algebraic \& Geometric Topology},
+    VOLUME = {6},
+      YEAR = {2006},
+     PAGES = {1459--1469 (electronic)},
+      ISSN = {1472-2747},
+   MRCLASS = {57M27 (18E05 57M25)},
+  MRNUMBER = {MR2253455},
+      note = {arXiv:\arxiv{math.GT/0606542}},
+}
+
+%S! fix this citation!
+@article{morrison-walker,
+    AUTHOR = {Scott Morrison and Kevin Walker},
+    TITLE = {Fixing the functoriality of Khovanov homology},
+     note = {\url{http://scott-morrison.org/functoriality}},
+}
+
+@misc{kw:tqft,
+    AUTHOR = {Walker, Kevin},
+    TITLE  = {Topological Quantum Field Theories},
+    URL    = {http://canyon23.net/math/tc.pdf},
+}
+
+@article{math.GT/0206303,
+    title = {{An invariant of link cobordisms from Khovanov homology}},
+    author = {Magnus Jacobsson},
+    journal = {Algebr. Geom. Topol.},
+    volume = 4,
+    year = 2004,
+    pages = {1211--1251},
+    note = {arXiv:\arxiv{math.GT/0206303}}}
+
+@misc{math.GT/0610650,
+    title = {{Khovanov-Rozansky homology via a canopolis formalism}},
+    author = {Ben Webster},
+      note = {arXiv:\arxiv{math.GT/0610650}}}
+
+@misc{green-implementation,
+    title = {{JavaKh}},
+    author= {Jeremey Green},
+    note = {\url{http://katlas.math.toronto.edu/wiki/Khovanov_Homology}},
+}
+
+@misc{ortiz-navarro,
+    title = {{Khovanov Homology and Reidemeister Torsion}},
+    author ={Juan Ariel Ortiz-Navarro and Chris Truman},
+    note = {a talk at the 2006 Toronto CMS meeting, slides at \url{http://www.math.uiowa.edu/~jortizna/Present-CMS-06.pdf}},
+}
+
+@book {MR1438306,
+    AUTHOR = {Gelfand, Sergei I. and Manin, Yuri I.},
+     TITLE = {Methods of homological algebra},
+      NOTE = {Translated from the 1988 Russian original},
+ PUBLISHER = {Springer-Verlag},
+   ADDRESS = {Berlin},
+      YEAR = {1996},
+     PAGES = {xviii+372},
+      ISBN = {3-540-54746-0},
+   MRCLASS = {18-02 (18Exx 18Gxx 55U35)},
+  MRNUMBER = {MR1438306 (97j:18001)},
+}

Binary file blob1.pdf has changed

--- a/blob1.tex	Tue Apr 22 05:13:02 2008 +0000
+++ b/blob1.tex	Thu Apr 24 02:56:34 2008 +0000
@@ -1,14 +1,14 @@
-\documentclass[11pt,leqno]{article}
+\documentclass[11pt,leqno]{amsart}
 
-\usepackage{amsmath,amssymb,amsthm}
-
-\usepackage[all]{xy}
+\newcommand{\pathtotrunk}{./}
+\input{text/article_preamble.tex}
+\input{text/top_matter.tex}
 
 % test edit #3
 
 %%%%% excerpts from my include file of standard macros
 
-\def\bc{{\cal B}}
+\def\bc{{\mathcal B}}
 
 \def\z{\mathbb{Z}}
 \def\r{\mathbb{R}}
@@ -38,23 +38,23 @@
 % tricky way to iterate macros over a list
 \def\semicolon{;}
 \def\applytolist#1{
-	\expandafter\def\csname multi#1\endcsname##1{
-		\def\multiack{##1}\ifx\multiack\semicolon
-			\def\next{\relax}
-		\else
-			\csname #1\endcsname{##1}
-			\def\next{\csname multi#1\endcsname}
-		\fi
-		\next}
-	\csname multi#1\endcsname}
+    \expandafter\def\csname multi#1\endcsname##1{
+        \def\multiack{##1}\ifx\multiack\semicolon
+            \def\next{\relax}
+        \else
+            \csname #1\endcsname{##1}
+            \def\next{\csname multi#1\endcsname}
+        \fi
+        \next}
+    \csname multi#1\endcsname}
 
 % \def\cA{{\cal A}} for A..Z
-\def\calc#1{\expandafter\def\csname c#1\endcsname{{\cal #1}}}
+\def\calc#1{\expandafter\def\csname c#1\endcsname{{\mathcal #1}}}
 \applytolist{calc}QWERTYUIOPLKJHGFDSAZXCVBNM;
 
 % \DeclareMathOperator{\pr}{pr} etc.
 \def\declaremathop#1{\expandafter\DeclareMathOperator\csname #1\endcsname{#1}}
-\applytolist{declaremathop}{pr}{im}{id}{gl}{tr}{rot}{Eq}{obj}{mor}{ob}{Rep}{End}{Hom}{Mat}{Tet}{cat}{Diff}{sign};
+\applytolist{declaremathop}{pr}{im}{id}{gl}{tr}{rot}{Eq}{obj}{mor}{ob}{Rep}{Tet}{cat}{Diff}{sign};
 
 
 
@@ -74,12 +74,6 @@
 \@addtoreset{equation}{section}
 \gdef\theequation{\thesection.\arabic{equation}}
 \makeatother
-\newtheorem{thm}[equation]{Theorem}
-\newtheorem{prop}[equation]{Proposition}
-\newtheorem{lemma}[equation]{Lemma}
-\newtheorem{cor}[equation]{Corollary}
-\newtheorem{defn}[equation]{Definition}
-
 
 
 \maketitle
@@ -88,10 +82,10 @@
 
 (motivation, summary/outline, etc.)
 
-(motivation: 
+(motivation:
 (1) restore exactness in pictures-mod-relations;
 (1') add relations-amongst-relations etc. to pictures-mod-relations;
-(2) want answer independent of handle decomp (i.e. don't 
+(2) want answer independent of handle decomp (i.e. don't
 just go from coend to derived coend (e.g. Hochschild homology));
 (3) ...
 )
@@ -102,35 +96,35 @@
 
 Fix a top dimension $n$.
 
-A {\it system of fields} 
+A {\it system of fields}
 \nn{maybe should look for better name; but this is the name I use elsewhere}
 is a collection of functors $\cC$ from manifolds of dimension $n$ or less
 to sets.
 These functors must satisfy various properties (see KW TQFT notes for details).
-For example: 
+For example:
 there is a canonical identification $\cC(X \du Y) = \cC(X) \times \cC(Y)$;
 there is a restriction map $\cC(X) \to \cC(\bd X)$;
 gluing manifolds corresponds to fibered products of fields;
-given a field $c \in \cC(Y)$ there is a ``product field" 
+given a field $c \in \cC(Y)$ there is a ``product field"
 $c\times I \in \cC(Y\times I)$; ...
 \nn{should eventually include full details of definition of fields.}
 
-\nn{note: probably will suppress from notation the distinction 
+\nn{note: probably will suppress from notation the distinction
 between fields and their (orientation-reversal) duals}
 
 \nn{remark that if top dimensional fields are not already linear
 then we will soon linearize them(?)}
 
-The definition of a system of fields is intended to generalize 
+The definition of a system of fields is intended to generalize
 the relevant properties of the following two examples of fields.
 
 The first example: Fix a target space $B$ and define $\cC(X)$ (where $X$
-is a manifold of dimension $n$ or less) to be the set of 
+is a manifold of dimension $n$ or less) to be the set of
 all maps from $X$ to $B$.
 
 The second example will take longer to explain.
-Given an $n$-category $C$ with the right sort of duality 
-(e.g. pivotal 2-category, 1-category with duals, star 1-category, disklike $n$-category), 
+Given an $n$-category $C$ with the right sort of duality
+(e.g. pivotal 2-category, 1-category with duals, star 1-category, disklike $n$-category),
 we can construct a system of fields as follows.
 Roughly speaking, $\cC(X)$ will the set of all embedded cell complexes in $X$
 with codimension $i$ cells labeled by $i$-morphisms of $C$.
@@ -149,18 +143,18 @@
 an object (0-morphism) of the 1-category $C$.
 A field on a 1-manifold $S$ consists of
 \begin{itemize}
-	\item A cell decomposition of $S$ (equivalently, a finite collection
+    \item A cell decomposition of $S$ (equivalently, a finite collection
 of points in the interior of $S$);
-	\item a labeling of each 1-cell (and each half 1-cell adjacent to $\bd S$)
+    \item a labeling of each 1-cell (and each half 1-cell adjacent to $\bd S$)
 by an object (0-morphism) of $C$;
-	\item a transverse orientation of each 0-cell, thought of as a choice of
+    \item a transverse orientation of each 0-cell, thought of as a choice of
 ``domain" and ``range" for the two adjacent 1-cells; and
-	\item a labeling of each 0-cell by a morphism (1-morphism) of $C$, with
+    \item a labeling of each 0-cell by a morphism (1-morphism) of $C$, with
 domain and range determined by the transverse orientation and the labelings of the 1-cells.
 \end{itemize}
 
 If $C$ is an algebra (i.e. if $C$ has only one 0-morphism) we can ignore the labels
-of 1-cells, so a field on a 1-manifold $S$ is a finite collection of points in the 
+of 1-cells, so a field on a 1-manifold $S$ is a finite collection of points in the
 interior of $S$, each transversely oriented and each labeled by an element (1-morphism)
 of the algebra.
 
@@ -175,19 +169,19 @@
 A field of a 1-manifold is defined as in the $n=1$ case, using the 0- and 1-morphisms of $C$.
 A field on a 2-manifold $Y$ consists of
 \begin{itemize}
-	\item A cell decomposition of $Y$ (equivalently, a graph embedded in $Y$ such
+    \item A cell decomposition of $Y$ (equivalently, a graph embedded in $Y$ such
 that each component of the complement is homeomorphic to a disk);
-	\item a labeling of each 2-cell (and each partial 2-cell adjacent to $\bd Y$)
+    \item a labeling of each 2-cell (and each partial 2-cell adjacent to $\bd Y$)
 by a 0-morphism of $C$;
-	\item a transverse orientation of each 1-cell, thought of as a choice of
+    \item a transverse orientation of each 1-cell, thought of as a choice of
 ``domain" and ``range" for the two adjacent 2-cells;
-	\item a labeling of each 1-cell by a 1-morphism of $C$, with
-domain and range determined by the transverse orientation of the 1-cell 
+    \item a labeling of each 1-cell by a 1-morphism of $C$, with
+domain and range determined by the transverse orientation of the 1-cell
 and the labelings of the 2-cells;
-	\item for each 0-cell, a homeomorphism of the boundary $R$ of a small neighborhood 
+    \item for each 0-cell, a homeomorphism of the boundary $R$ of a small neighborhood
 of the 0-cell to $S^1$ such that the intersections of the 1-cells with $R$ are not mapped
 to $\pm 1 \in S^1$; and
-	\item a labeling of each 0-cell by a 2-morphism of $C$, with domain and range 
+    \item a labeling of each 0-cell by a 2-morphism of $C$, with domain and range
 determined by the labelings of the 1-cells and the parameterizations of the previous
 bullet.
 \end{itemize}
@@ -195,10 +189,10 @@
 
 For general $n$, a field on a $k$-manifold $X^k$ consists of
 \begin{itemize}
-	\item A cell decomposition of $X$;
-	\item an explicit general position homeomorphism from the link of each $j$-cell
+    \item A cell decomposition of $X$;
+    \item an explicit general position homeomorphism from the link of each $j$-cell
 to the boundary of the standard $(k-j)$-dimensional bihedron; and
-	\item a labeling of each $j$-cell by a $(k-j)$-dimensional morphism of $C$, with
+    \item a labeling of each $j$-cell by a $(k-j)$-dimensional morphism of $C$, with
 domain and range determined by the labelings of the link of $j$-cell.
 \end{itemize}
 
@@ -208,10 +202,10 @@
 
 \medskip
 
-For top dimensional ($n$-dimensional) manifolds, we're actually interested 
+For top dimensional ($n$-dimensional) manifolds, we're actually interested
 in the linearized space of fields.
 By default, define $\cC_l(X) = \c[\cC(X)]$; that is, $\cC_l(X)$ is
-the vector space of finite 
+the vector space of finite
 linear combinations of fields on $X$.
 If $X$ has boundary, we of course fix a boundary condition: $\cC_l(X; a) = \c[\cC(X; a)]$.
 Thus the restriction (to boundary) maps are well defined because we never
@@ -220,9 +214,9 @@
 In some cases we don't linearize the default way; instead we take the
 spaces $\cC_l(X; a)$ to be part of the data for the system of fields.
 In particular, for fields based on linear $n$-category pictures we linearize as follows.
-Define $\cC_l(X; a) = \c[\cC(X; a)]/K$, where $K$ is the space generated by 
+Define $\cC_l(X; a) = \c[\cC(X; a)]/K$, where $K$ is the space generated by
 obvious relations on 0-cell labels.
-More specifically, let $L$ be a cell decomposition of $X$ 
+More specifically, let $L$ be a cell decomposition of $X$
 and let $p$ be a 0-cell of $L$.
 Let $\alpha_c$ and $\alpha_d$ be two labelings of $L$ which are identical except that
 $\alpha_c$ labels $p$ by $c$ and $\alpha_d$ labels $p$ by $d$.
@@ -231,9 +225,9 @@
 to infer the meaning of $\alpha_{\lambda c + d}$.
 Note that we are still assuming that $n$-categories have linear spaces of $n$-morphisms.
 
-\nn{Maybe comment further: if there's a natural basis of morphisms, then no need; 
+\nn{Maybe comment further: if there's a natural basis of morphisms, then no need;
 will do something similar below; in general, whenever a label lives in a linear
-space we do something like this; ? say something about tensor 
+space we do something like this; ? say something about tensor
 product of all the linear label spaces?  Yes:}
 
 For top dimensional ($n$-dimensional) manifolds, we linearize as follows.
@@ -243,7 +237,7 @@
 space determined by the labeling of the link of the 0-cell.
 (If the 0-cell were labeled, the label would live in this space.)
 We associate to each almost-labeling the tensor product of these spaces (one for each 0-cell).
-We now define $\cC_l(X; a)$ to be the direct sum over all almost labelings of the 
+We now define $\cC_l(X; a)$ to be the direct sum over all almost labelings of the
 above tensor products.
 
 
@@ -251,12 +245,12 @@
 \subsection{Local relations}
 
 Let $B^n$ denote the standard $n$-ball.
-A {\it local relation} is a collection subspaces $U(B^n; c) \sub \cC_l(B^n; c)$ 
+A {\it local relation} is a collection subspaces $U(B^n; c) \sub \cC_l(B^n; c)$
 (for all $c \in \cC(\bd B^n)$) satisfying the following (three?) properties.
 
-\nn{Roughly, these are (1) the local relations imply (extended) isotopy; 
+\nn{Roughly, these are (1) the local relations imply (extended) isotopy;
 (2) $U(B^n; \cdot)$ is an ideal w.r.t.\ gluing; and
-(3) this ideal is generated by ``small" generators (contained in an open cover of $B^n$). 
+(3) this ideal is generated by ``small" generators (contained in an open cover of $B^n$).
 See KW TQFT notes for details.  Need to transfer details to here.}
 
 For maps into spaces, $U(B^n; c)$ is generated by things of the form $a-b \in \cC_l(B^n; c)$,
@@ -292,7 +286,7 @@
 In this section we will usually suppress boundary conditions on $X$ from the notation
 (e.g. write $\cC_l(X)$ instead of $\cC_l(X; c)$).
 
-We only consider compact manifolds, so if $Y \sub X$ is a closed codimension 0 
+We only consider compact manifolds, so if $Y \sub X$ is a closed codimension 0
 submanifold of $X$, then $X \setmin Y$ implicitly means the closure
 $\overline{X \setmin Y}$.
 
@@ -326,7 +320,7 @@
 
 There is a map $\bd : \bc_1(X) \to \bc_0(X)$ which sends $(B, r, u)$ to $ru$, the linear
 combination of fields on $X$ obtained by gluing $r$ to $u$.
-In other words $\bd : \bc_1(X) \to \bc_0(X)$ is given by 
+In other words $\bd : \bc_1(X) \to \bc_0(X)$ is given by
 just erasing the blob from the picture
 (but keeping the blob label $u$).
 
@@ -334,7 +328,7 @@
 is naturally isomorphic to $\bc_0(X)/\bd(\bc_1(X))) = H_0(\bc_*(X))$.
 
 $\bc_2(X)$ is the space of all relations (redundancies) among the relations of $\bc_1(X)$.
-More specifically, $\bc_2(X)$ is the space of all finite linear combinations of 
+More specifically, $\bc_2(X)$ is the space of all finite linear combinations of
 2-blob diagrams (defined below), modulo the usual linear label relations.
 \nn{and also modulo blob reordering relations?}
 
@@ -403,14 +397,14 @@
 Let $x_a$ be the blob diagram with label $a$, and define $x_b$ and $x_c$ similarly.
 Then we impose the relation
 \eq{
-	x_c = \lambda x_a + x_b .
+    x_c = \lambda x_a + x_b .
 }
 \nn{should do this in terms of direct sums of tensor products}
 Let $x$ and $x'$ be two blob diagrams which differ only by a permutation $\pi$
 of their blob labelings.
 Then we impose the relation
 \eq{
-	x = \sign(\pi) x' .
+    x = \sign(\pi) x' .
 }
 
 (Alert readers will have noticed that for $k=2$ our definition
@@ -430,7 +424,7 @@
 where $r_l$ is the restriction of $r$ to $B_l \setmin B_j$.
 Finally, define
 \eq{
-	\bd(b) = \sum_{j=0}^{k-1} (-1)^j E_j(b).
+    \bd(b) = \sum_{j=0}^{k-1} (-1)^j E_j(b).
 }
 The $(-1)^j$ factors imply that the terms of $\bd^2(b)$ all cancel.
 Thus we have a chain complex.
@@ -438,8 +432,8 @@
 \nn{?? say something about the ``shape" of tree? (incl = cone, disj = product)}
 
 
-\nn{TO DO: 
-expand definition to handle DGA and $A_\infty$ versions of $n$-categories; 
+\nn{TO DO:
+expand definition to handle DGA and $A_\infty$ versions of $n$-categories;
 relations to Chas-Sullivan string stuff}
 
 
@@ -451,7 +445,7 @@
 \end{prop}
 \begin{proof}
 Given blob diagrams $b_1$ on $X$ and $b_2$ on $Y$, we can combine them
-(putting the $b_1$ blobs before the $b_2$ blobs in the ordering) to get a 
+(putting the $b_1$ blobs before the $b_2$ blobs in the ordering) to get a
 blob diagram $(b_1, b_2)$ on $X \du Y$.
 Because of the blob reordering relations, all blob diagrams on $X \du Y$ arise this way.
 In the other direction, any blob diagram on $X\du Y$ is equal (up to sign)
@@ -467,8 +461,8 @@
 For the next proposition we will temporarily restore $n$-manifold boundary
 conditions to the notation.
 
-Suppose that for all $c \in \cC(\bd B^n)$ 
-we have a splitting $s: H_0(\bc_*(B^n, c)) \to \bc_0(B^n; c)$ 
+Suppose that for all $c \in \cC(\bd B^n)$
+we have a splitting $s: H_0(\bc_*(B^n, c)) \to \bc_0(B^n; c)$
 of the quotient map
 $p: \bc_0(B^n; c) \to H_0(\bc_*(B^n, c))$.
 \nn{always the case if we're working over $\c$}.
@@ -490,7 +484,7 @@
 \nn{$x$ is a 0-blob diagram, i.e. $x \in \cC(B^n; c)$}
 \end{proof}
 
-(Note that for the above proof to work, we need the linear label relations 
+(Note that for the above proof to work, we need the linear label relations
 for blob labels.
 Also we need to blob reordering relations (?).)
 
@@ -525,7 +519,7 @@
 
 \begin{prop}
 For fixed fields ($n$-cat), $\bc_*$ is a functor from the category
-of $n$-manifolds and diffeomorphisms to the category of chain complexes and 
+of $n$-manifolds and diffeomorphisms to the category of chain complexes and
 (chain map) isomorphisms.
 \qed
 \end{prop}
@@ -558,9 +552,9 @@
 \begin{prop}
 There is a natural chain map
 \eq{
-	\gl: \bigoplus_a \bc_*(X; a, -a, c) \to \bc_*(X\sgl; c\sgl).
+    \gl: \bigoplus_a \bc_*(X; a, -a, c) \to \bc_*(X\sgl; c\sgl).
 }
-The sum is over all fields $a$ on $Y$ compatible at their 
+The sum is over all fields $a$ on $Y$ compatible at their
 ($n{-}2$-dimensional) boundaries with $c$.
 `Natural' means natural with respect to the actions of diffeomorphisms.
 \qed
@@ -574,7 +568,7 @@
 (Typically one of $X_1$ or $X_2$ is a disjoint union of balls.)
 For $x_i \in \bc_*(X_i)$, we introduce the notation
 \eq{
-	x_1 \bullet x_2 \deq \gl(x_1 \otimes x_2) .
+    x_1 \bullet x_2 \deq \gl(x_1 \otimes x_2) .
 }
 Note that we have resumed our habit of omitting boundary labels from the notation.
 
@@ -589,17 +583,17 @@
 \section{$n=1$ and Hochschild homology}
 
 In this section we analyze the blob complex in dimension $n=1$
-and find that for $S^1$ the homology of the blob complex is the 
+and find that for $S^1$ the homology of the blob complex is the
 Hochschild homology of the category (algebroid) that we started with.
 \nn{or maybe say here that the complexes are quasi-isomorphic?  in general,
 should perhaps put more emphasis on the complexes and less on the homology.}
 
 Notation: $HB_i(X) = H_i(\bc_*(X))$.
 
-Let us first note that there is no loss of generality in assuming that our system of 
+Let us first note that there is no loss of generality in assuming that our system of
 fields comes from a category.
 (Or maybe (???) there {\it is} a loss of generality.
-Given any system of fields, $A(I; a, b) = \cC(I; a, b)/U(I; a, b)$ can be 
+Given any system of fields, $A(I; a, b) = \cC(I; a, b)/U(I; a, b)$ can be
 thought of as the morphisms of a 1-category $C$.
 More specifically, the objects of $C$ are $\cC(pt)$, the morphisms from $a$ to $b$
 are $A(I; a, b)$, and composition is given by gluing.
@@ -624,7 +618,7 @@
 \begin{itemize}
 \item $\cC(pt) = \ob(C)$ .
 \item Let $R$ be a 1-manifold and $c \in \cC(\bd R)$.
-Then an element of $\cC(R; c)$ is a collection of (transversely oriented) 
+Then an element of $\cC(R; c)$ is a collection of (transversely oriented)
 points in the interior
 of $R$, each labeled by a morphism of $C$.
 The intervals between the points are labeled by objects of $C$, consistent with
@@ -635,12 +629,12 @@
 the same way.
 \item For $x \in \mor(a, b)$ let $\chi(x) \in \cC(I; a, b)$ be the field with a single
 point (at some standard location) labeled by $x$.
-Then the kernel of the evaluation map $U(I; a, b)$ is generated by things of the 
+Then the kernel of the evaluation map $U(I; a, b)$ is generated by things of the
 form $y - \chi(e(y))$.
 Thus we can, if we choose, restrict the blob twig labels to things of this form.
 \end{itemize}
 
-We want to show that $HB_*(S^1)$ is naturally isomorphic to the 
+We want to show that $HB_*(S^1)$ is naturally isomorphic to the
 Hochschild homology of $C$.
 \nn{Or better that the complexes are homotopic
 or quasi-isomorphic.}
@@ -691,13 +685,13 @@
 First we show that $F_*(C\otimes C)$ is
 quasi-isomorphic to the 0-step complex $C$.
 
-Let $F'_* \sub F_*(C\otimes C)$ be the subcomplex where the label of  
+Let $F'_* \sub F_*(C\otimes C)$ be the subcomplex where the label of
 the point $*$ is $1 \otimes 1 \in C\otimes C$.
 We will show that the inclusion $i: F'_* \to F_*(C\otimes C)$ is a quasi-isomorphism.
 
 Fix a small $\ep > 0$.
 Let $B_\ep$ be the ball of radius $\ep$ around $* \in S^1$.
-Let $F^\ep_* \sub F_*(C\otimes C)$ be the subcomplex 
+Let $F^\ep_* \sub F_*(C\otimes C)$ be the subcomplex
 generated by blob diagrams $b$ such that $B_\ep$ is either disjoint from
 or contained in each blob of $b$, and the two boundary points of $B_\ep$ are not labeled points of $b$.
 For a field (picture) $y$ on $B_\ep$, let $s_\ep(y)$ be the equivalent picture with~$*$
@@ -712,7 +706,7 @@
 $x$ as a new twig blob, with label $y - s_\ep(y)$, where $y$ is the restriction of $x$ to $B_\ep$.
 If $*$ is contained in a twig blob $B$ with label $u = \sum z_i$, $j_\ep(x)$ is obtained as follows.
 Let $y_i$ be the restriction of $z_i$ to $B_\ep$.
-Let $x_i$ be equal to $x$ outside of $B$, equal to $z_i$ on $B \setmin B_\ep$, 
+Let $x_i$ be equal to $x$ outside of $B$, equal to $z_i$ on $B \setmin B_\ep$,
 and have an additional blob $B_\ep$ with label $y_i - s_\ep(y_i)$.
 Define $j_\ep(x) = \sum x_i$.
 \nn{need to check signs coming from blob complex differential}
@@ -721,7 +715,7 @@
 
 The key property of $j_\ep$ is
 \eq{
-	\bd j_\ep + j_\ep \bd = \id - \sigma_\ep ,
+    \bd j_\ep + j_\ep \bd = \id - \sigma_\ep ,
 }
 where $\sigma_\ep : F^\ep_* \to F^\ep_*$ is given by replacing the restriction $y$ of each field
 mentioned in $x \in F^\ep_*$ with $s_\ep(y)$.
@@ -731,10 +725,10 @@
 is a homotopy inverse to the inclusion $F'_* \to F_*(C\otimes C)$.
 One strategy would be to try to stitch together various $j_\ep$ for progressively smaller
 $\ep$ and show that $F'_*$ is homotopy equivalent to $F_*(C\otimes C)$.
-Instead, we'll be less ambitious and just show that 
+Instead, we'll be less ambitious and just show that
 $F'_*$ is quasi-isomorphic to $F_*(C\otimes C)$.
 
-If $x$ is a cycle in $F_*(C\otimes C)$, then for sufficiently small $\ep$ we have 
+If $x$ is a cycle in $F_*(C\otimes C)$, then for sufficiently small $\ep$ we have
 $x \in F_*^\ep$.
 (This is true for any chain in $F_*(C\otimes C)$, since chains are sums of
 finitely many blob diagrams.)
@@ -743,7 +737,7 @@
 If $y \in F_*(C\otimes C)$ and $\bd y = x \in F'_*$, then $y \in F^\ep_*$ for some $\ep$
 and
 \eq{
-	\bd y = \bd (\sigma_\ep(y) + j_\ep(x)) .
+    \bd y = \bd (\sigma_\ep(y) + j_\ep(x)) .
 }
 Since $\sigma_\ep(y) + j_\ep(x) \in F'$, it follows that the inclusion map is injective on homology.
 This completes the proof that $F'_*$ is quasi-isomorphic to $F_*(C\otimes C)$.
@@ -769,7 +763,7 @@
 Next we construct a degree 1 map (homotopy) $h: F'_* \to F'_*$ such that
 for all $x \in F'_*$ we have
 \eq{
-	x - \bd h(x) - h(\bd x) \in F''_* .
+    x - \bd h(x) - h(\bd x) \in F''_* .
 }
 Since $F'_0 = F''_0$, we can take $h_0 = 0$.
 Let $x \in F'_1$, with single blob $B \sub S^1$.
@@ -793,7 +787,7 @@
 Finally, we show that $F''_*$ is contractible.
 \nn{need to also show that $H_0$ is the right thing; easy, but I won't do it now}
 Let $x$ be a cycle in $F''_*$.
-The union of the supports of the diagrams in $x$ does not contain $*$, so there exists a 
+The union of the supports of the diagrams in $x$ does not contain $*$, so there exists a
 ball $B \subset S^1$ containing the union of the supports and not containing $*$.
 Adding $B$ as a blob to $x$ gives a contraction.
 \nn{need to say something else in degree zero}
@@ -813,11 +807,11 @@
 * is a labeled point in $y$.
 Otherwise, define $s(y)$ to be the result of adding a label 1 (identity morphism) at *.
 Let $x \in \bc_*(S^1)$.
-Let $s(x)$ be the result of replacing each field $y$ (containing *) mentioned in 
+Let $s(x)$ be the result of replacing each field $y$ (containing *) mentioned in
 $x$ with $y$.
 It is easy to check that $s$ is a chain map and $s \circ i = \id$.
 
-Let $G^\ep_* \sub \bc_*(S^1)$ be the subcomplex where there are no labeled points 
+Let $G^\ep_* \sub \bc_*(S^1)$ be the subcomplex where there are no labeled points
 in a neighborhood $B_\ep$ of *, except perhaps *.
 Note that for any chain $x \in \bc_*(S^1)$, $x \in G^\ep_*$ for sufficiently small $\ep$.
 \nn{rest of argument goes similarly to above}
@@ -833,8 +827,36 @@
 Probably it's worth writing down an explicit map even if we don't need to.}
 
 
+We can also describe explicitly a map from the standard Hochschild
+complex to the blob complex on the circle. \nn{What properties does this
+map have?}
 
+\begin{figure}%
+$$\mathfig{0.6}{barycentric/barycentric}$$
+\caption{The Hochschild chain $a \tensor b \tensor c$ is sent to
+the sum of six blob $2$-chains, corresponding to a barycentric subdivision of a $2$-simplex.}
+\label{fig:Hochschild-example}%
+\end{figure}
 
+As an example, Figure \ref{fig:Hochschild-example} shows the image of the Hochschild chain $a \tensor b \tensor c$. Only the $0$-cells are shown explicitly.
+The edges marked $x, y$ and $z$ carry the $1$-chains
+\begin{align*}
+x & = \mathfig{0.1}{barycentric/ux} & u_x = \mathfig{0.1}{barycentric/ux_ca} - \mathfig{0.1}{barycentric/ux_c-a} \\
+y & = \mathfig{0.1}{barycentric/uy} & u_y = \mathfig{0.1}{barycentric/uy_cab} - \mathfig{0.1}{barycentric/uy_ca-b} \\
+z & = \mathfig{0.1}{barycentric/uz} & u_z = \mathfig{0.1}{barycentric/uz_c-a-b} - \mathfig{0.1}{barycentric/uz_cab}
+\end{align*}
+and the $2$-chain labelled $A$ is
+\begin{equation*}
+A = \mathfig{0.1}{barycentric/Ax}+\mathfig{0.1}{barycentric/Ay}.
+\end{equation*}
+Note that we then have
+\begin{equation*}
+\bdy A = x+y+z.
+\end{equation*}
+
+In general, the Hochschild chain $\Tensor_{i=1}^n a_i$ is sent to the sum of $n!$ blob $(n-1)$-chains, indexed by permutations,
+$$\phi\left(\Tensor_{i=1}^n a_i) = \sum_{\pi} \phi^\pi(a_1, \ldots, a_n)$$
+with ...
 
 
 \section{Action of $C_*(\Diff(X))$}  \label{diffsect}
@@ -849,16 +871,16 @@
 \begin{prop}  \label{CDprop}
 For each $n$-manifold $X$ there is a chain map
 \eq{
-	e_X : CD_*(X) \otimes \bc_*(X) \to \bc_*(X) .
+    e_X : CD_*(X) \otimes \bc_*(X) \to \bc_*(X) .
 }
 On $CD_0(X) \otimes \bc_*(X)$ it agrees with the obvious action of $\Diff(X)$ on $\bc_*(X)$
 (Proposition (\ref{diff0prop})).
 For any splitting $X = X_1 \cup X_2$, the following diagram commutes
 \eq{ \xymatrix{
-	 CD_*(X) \otimes \bc_*(X) \ar[r]^{e_X}    & \bc_*(X) \\
-	 CD_*(X_1) \otimes CD_*(X_2) \otimes \bc_*(X_1) \otimes \bc_*(X_2) 
-	 	\ar@/_4ex/[r]_{e_{X_1} \otimes e_{X_2}}  \ar[u]^{\gl \otimes \gl}  & 
-			\bc_*(X_1) \otimes \bc_*(X_2) \ar[u]_{\gl}
+     CD_*(X) \otimes \bc_*(X) \ar[r]^{e_X}    & \bc_*(X) \\
+     CD_*(X_1) \otimes CD_*(X_2) \otimes \bc_*(X_1) \otimes \bc_*(X_2)
+        \ar@/_4ex/[r]_{e_{X_1} \otimes e_{X_2}}  \ar[u]^{\gl \otimes \gl}  &
+            \bc_*(X_1) \otimes \bc_*(X_2) \ar[u]_{\gl}
 } }
 Any other map satisfying the above two properties is homotopic to $e_X$.
 \end{prop}
@@ -876,18 +898,18 @@
 A $k$-parameter family of diffeomorphisms $f: P \times X \to X$ is
 {\it adapted to $\cU$} if there is a factorization
 \eq{
-	P = P_1 \times \cdots \times P_m
+    P = P_1 \times \cdots \times P_m
 }
 (for some $m \le k$)
 and families of diffeomorphisms
 \eq{
-	f_i :  P_i \times X \to X
+    f_i :  P_i \times X \to X
 }
-such that 
+such that
 \begin{itemize}
 \item each $f_i(p, \cdot): X \to X$ is supported on some connected $V_i \sub X$;
 \item the $V_i$'s are mutually disjoint;
-\item each $V_i$ is the union of at most $k_i$ of the $U_\alpha$'s, 
+\item each $V_i$ is the union of at most $k_i$ of the $U_\alpha$'s,
 where $k_i = \dim(P_i)$; and
 \item $f(p, \cdot) = f_1(p_1, \cdot) \circ \cdots \circ f_m(p_m, \cdot) \circ g$
 for all $p = (p_1, \ldots, p_m)$, for some fixed $g \in \Diff(X)$.
@@ -904,12 +926,12 @@
 
 \medskip
 
-Let $B_1, \ldots, B_m$ be a collection of disjoint balls in $X$ 
+Let $B_1, \ldots, B_m$ be a collection of disjoint balls in $X$
 (e.g.~the support of a blob diagram).
 We say that $f:P\times X\to X$ is {\it compatible} with $\{B_j\}$ if
 $f$ has support a disjoint collection of balls $D_i \sub X$ and for all $i$ and $j$
 either $B_j \sub D_i$ or $B_j \cap D_i = \emptyset$.
-A chain $x \in CD_k(X)$ is compatible with $\{B_j\}$ if it is a sum of singular cells, 
+A chain $x \in CD_k(X)$ is compatible with $\{B_j\}$ if it is a sum of singular cells,
 each of which is compatible.
 (Note that we could strengthen the definition of compatibility to incorporate
 a factorization condition, similar to the definition of ``adapted to" above.
@@ -920,14 +942,14 @@
 Then $x$ is homotopic (rel boundary) to some $x' \in CD_k(X)$ which is compatible with $\{B_j\}$.
 \end{cor}
 \begin{proof}
-This will follow from Lemma \ref{extension_lemma} for 
+This will follow from Lemma \ref{extension_lemma} for
 appropriate choice of cover $\cU = \{U_\alpha\}$.
 Let $U_{\alpha_1}, \ldots, U_{\alpha_k}$ be any $k$ open sets of $\cU$, and let
 $V_1, \ldots, V_m$ be the connected components of $U_{\alpha_1}\cup\cdots\cup U_{\alpha_k}$.
 Choose $\cU$ fine enough so that there exist disjoint balls $B'_j \sup B_j$ such that for all $i$ and $j$
 either $V_i \sub B'_j$ or $V_i \cap B'_j = \emptyset$.
 
-Apply Lemma \ref{extension_lemma} first to each singular cell $f_i$ of $\bd x$, 
+Apply Lemma \ref{extension_lemma} first to each singular cell $f_i$ of $\bd x$,
 with the (compatible) support of $f_i$ in place of $X$.
 This insures that the resulting homotopy $h_i$ is compatible.
 Now apply Lemma \ref{extension_lemma} to $x + \sum h_i$.
@@ -957,7 +979,7 @@
 \nn{not sure what the best way to deal with boundary is; for now just give main argument, worry
 about boundary later}
 
-Recall that we are given 
+Recall that we are given
 an open cover $\cU = \{U_\alpha\}$ and an
 $x \in CD_k(X)$ such that $\bd x$ is adapted to $\cU$.
 We must find a homotopy of $x$ (rel boundary) to some $x' \in CD_k(X)$ which is adapted to $\cU$.
@@ -965,20 +987,20 @@
 Let $\{r_\alpha : X \to [0,1]\}$ be a partition of unity for $\cU$.
 
 As a first approximation to the argument we will eventually make, let's replace $x$
-with a single singular cell 
+with a single singular cell
 \eq{
-	f: P \times X \to X .
+    f: P \times X \to X .
 }
 Also, we'll ignore for now issues around $\bd P$.
 
 Our homotopy will have the form
 \eqar{
-	F: I \times P \times X &\to& X \\
-	(t, p, x) &\mapsto& f(u(t, p, x), x)
+    F: I \times P \times X &\to& X \\
+    (t, p, x) &\mapsto& f(u(t, p, x), x)
 }
 for some function
 \eq{
-	u : I \times P \times X \to P .
+    u : I \times P \times X \to P .
 }
 First we describe $u$, then we argue that it does what we want it to do.
 
@@ -1007,16 +1029,16 @@
 
 For $p \in D$ we define
 \eq{
-	u(t, p, x) = (1-t)p + t \sum_\alpha r_\alpha(x) p_{c_\alpha} .
+    u(t, p, x) = (1-t)p + t \sum_\alpha r_\alpha(x) p_{c_\alpha} .
 }
 (Recall that $P$ is a single linear cell, so the weighted average of points of $P$
 makes sense.)
 
 So far we have defined $u(t, p, x)$ when $p$ lies in a $k$-handle of $J$.
-For handles of $J$ of index less than $k$, we will define $u$ to 
+For handles of $J$ of index less than $k$, we will define $u$ to
 interpolate between the values on $k$-handles defined above.
 
-If $p$ lies in a $k{-}1$-handle $E$, let $\eta : E \to [0,1]$ be the normal coordinate 
+If $p$ lies in a $k{-}1$-handle $E$, let $\eta : E \to [0,1]$ be the normal coordinate
 of $E$.
 In particular, $\eta$ is equal to 0 or 1 only at the intersection of $E$
 with a $k$-handle.
@@ -1026,8 +1048,8 @@
 adjacent to the $k{-}1$-cell corresponding to $E$.
 For $p \in E$, define
 \eq{
-	u(t, p, x) = (1-t)p + t \left( \sum_{\alpha \ne \beta} r_\alpha(x) p_{c_\alpha}
-			+ r_\beta(x) (\eta(p) q_1 + (1-\eta(p)) q_0) \right) .
+    u(t, p, x) = (1-t)p + t \left( \sum_{\alpha \ne \beta} r_\alpha(x) p_{c_\alpha}
+            + r_\beta(x) (\eta(p) q_1 + (1-\eta(p)) q_0) \right) .
 }
 
 In general, for $E$ a $k{-}j$-handle, there is a normal coordinate
@@ -1040,10 +1062,10 @@
 For each $\beta \in \cN$, let $\{q_{\beta i}\}$ be the set of points in $P$ associated to the aforementioned $k$-cells.
 Now define, for $p \in E$,
 \eq{
-	u(t, p, x) = (1-t)p + t \left( 
-			\sum_{\alpha \notin \cN} r_\alpha(x) p_{c_\alpha}
-				+ \sum_{\beta \in \cN} r_\beta(x) \left( \sum_i \eta_{\beta i}(p) \cdot q_{\beta i} \right)
-			 \right) .
+    u(t, p, x) = (1-t)p + t \left(
+            \sum_{\alpha \notin \cN} r_\alpha(x) p_{c_\alpha}
+                + \sum_{\beta \in \cN} r_\beta(x) \left( \sum_i \eta_{\beta i}(p) \cdot q_{\beta i} \right)
+             \right) .
 }
 Here $\eta_{\beta i}(p)$ is the weight given to $q_{\beta i}$ by the linear extension
 mentioned above.
@@ -1062,8 +1084,8 @@
 We must show that the derivative $\pd{F}{x}(t, p, x)$ is non-singular for all $(t, p, x)$.
 We have
 \eq{
-%	\pd{F}{x}(t, p, x) = \pd{f}{x}(u(t, p, x), x) + \pd{f}{p}(u(t, p, x), x) \pd{u}{x}(t, p, x) .
-	\pd{F}{x} = \pd{f}{x} + \pd{f}{p} \pd{u}{x} .
+%   \pd{F}{x}(t, p, x) = \pd{f}{x}(u(t, p, x), x) + \pd{f}{p}(u(t, p, x), x) \pd{u}{x}(t, p, x) .
+    \pd{F}{x} = \pd{f}{x} + \pd{f}{p} \pd{u}{x} .
 }
 Since $f$ is a family of diffeomorphisms, $\pd{f}{x}$ is non-singular and
 \nn{bounded away from zero, or something like that}.
@@ -1083,7 +1105,7 @@
 This will complete the proof of the lemma.
 \nn{except for boundary issues and the `$P$ is a cell' assumption}
 
-Let $j$ be the codimension of $D$. 
+Let $j$ be the codimension of $D$.
 (Or rather, the codimension of its corresponding cell.  From now on we will not make a distinction
 between handle and corresponding cell.)
 Then $j = j_1 + \cdots + j_m$, $0 \le m \le k$,
@@ -1110,7 +1132,7 @@
 The singular 1-cell is supported on $U_\beta$, since $r_\beta = 0$ outside of this set.
 
 Next case: $j=2$, $m=1$, $j_1 = 2$.
-This is similar to the previous case, except that the normal bundle is 2-dimensional instead of 
+This is similar to the previous case, except that the normal bundle is 2-dimensional instead of
 1-dimensional.
 We have that $D \to \Diff(X)$ is a product of a constant singular $k{-}2$-cell
 and a 2-cell with support $U_\beta$.
@@ -1136,15 +1158,15 @@
 \section{$A_\infty$ action on the boundary}
 
 Let $Y$ be an $n{-}1$-manifold.
-The collection of complexes $\{\bc_*(Y\times I; a, b)\}$, where $a, b \in \cC(Y)$ are boundary 
+The collection of complexes $\{\bc_*(Y\times I; a, b)\}$, where $a, b \in \cC(Y)$ are boundary
 conditions on $\bd(Y\times I) = Y\times \{0\} \cup Y\times\{1\}$, has the structure
 of an $A_\infty$ category.
 
 Composition of morphisms (multiplication) depends of a choice of homeomorphism
 $I\cup I \cong I$.  Given this choice, gluing gives a map
 \eq{
-	\bc_*(Y\times I; a, b) \otimes \bc_*(Y\times I; b, c) \to \bc_*(Y\times (I\cup I); a, c)
-			\cong \bc_*(Y\times I; a, c)
+    \bc_*(Y\times I; a, b) \otimes \bc_*(Y\times I; b, c) \to \bc_*(Y\times (I\cup I); a, c)
+            \cong \bc_*(Y\times I; a, c)
 }
 Using (\ref{CDprop}) and the inclusion $\Diff(I) \sub \Diff(Y\times I)$ gives the various
 higher associators of the $A_\infty$ structure, more or less canonically.
@@ -1155,7 +1177,7 @@
 
 Similarly, if $Y \sub \bd X$, a choice of collaring homeomorphism
 $(Y\times I) \cup_Y X \cong X$ gives the collection of complexes $\bc_*(X; r, a)$
-(variable $a \in \cC(Y)$; fixed $r \in \cC(\bd X \setmin Y)$) the structure of a representation of the 
+(variable $a \in \cC(Y)$; fixed $r \in \cC(\bd X \setmin Y)$) the structure of a representation of the
 $A_\infty$ category $\{\bc_*(Y\times I; \cdot, \cdot)\}$.
 Again the higher associators come from the action of $\Diff(I)$ on a collar neighborhood
 of $Y$ in $X$.
@@ -1176,14 +1198,14 @@
 Gluing the two copies of $Y$ together we obtain a new $n$-manifold $X\sgl$.
 We wish to describe the blob complex of $X\sgl$ in terms of the blob complex
 of $X$.
-More precisely, we want to describe $\bc_*(X\sgl; c\sgl)$, 
+More precisely, we want to describe $\bc_*(X\sgl; c\sgl)$,
 where $c\sgl \in \cC(\bd X\sgl)$,
 in terms of the collection $\{\bc_*(X; c, \cdot, \cdot)\}$, thought of as a representation
 of the $A_\infty$ category $\cA(Y\du-Y) \cong \cA(Y)\times \cA(Y)\op$.
 
 \begin{thm}
 $\bc_*(X\sgl; c\sgl)$ is quasi-isomorphic to the the self tensor product
-of $\{\bc_*(X; c, \cdot, \cdot)\}$ over $\cA(Y)$. 
+of $\{\bc_*(X; c, \cdot, \cdot)\}$ over $\cA(Y)$.
 \end{thm}
 
 The proof will occupy the remainder of this section.
@@ -1200,7 +1222,7 @@
 
 \section{Extension to ...}
 
-\nn{Need to let the input $n$-category $C$ be a graded thing 
+\nn{Need to let the input $n$-category $C$ be a graded thing
 (e.g.~DGA or $A_\infty$ $n$-category).}
 
 \nn{maybe this should be done earlier in the exposition?
@@ -1233,6 +1255,3 @@
 %$m: \bc_0(B^n; c, c') \to \mor(c, c')$.
 %If we regard $\mor(c, c')$ as a complex concentrated in degree 0, then this becomes a chain
 %map $m: \bc_*(B^n; c, c') \to \mor(c, c')$.
-
-
-

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/build.xml	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,96 @@
+<!-- This is an Ant build file; you'll need to install Ant before using it. -->
+<project name="su_3-functoriality" default="usage">
+    <target name="init">
+      <property name="arxivTarFile" value="su_3-functoriality.tar"/>
+    </target>
+
+    <!-- USAGE -->
+    <!-- Instructions for using the build file -->
+    <!-- =================================================================== -->
+    <target name = "usage" depends = "init">    
+        <echo message = ""/>
+        <echo message = "su_3-functoriality build instructions"/>
+        <echo message = "-------------------------------------------------------------"/>
+        <echo message = ""/>
+        <echo message = " available targets are:"/>
+        <echo message = ""/>
+        <echo message = "   arxiv --> builds su_3-functoriality.tar.gz, for submission to the arxiv"/>
+        <echo message = "   dvi   --> builds su_3-functoriality.dvi"/>
+        <echo message = "   ps    --> builds su_3-functoriality.ps"/>
+        <echo message = "   pdf   --> builds su_3-functoriality.pdf"/>
+        <echo message = ""/>
+        <echo message = "-------------------------------------------------------------"/>
+        <echo message = ""/>  
+    </target>
+    <!-- =================================================================== -->    
+
+    <target name="clean" depends="init">
+        <delete>
+            <fileset dir=".">
+                <include name="*.toc"/>
+                <include name="*.log"/>
+                <include name="*.aux"/>
+                <include name="*.blg"/>
+                <include name="*.xyc"/>
+                <include name="*.out"/>
+            </fileset>
+        </delete>
+    </target>
+
+    <target name="arxiv" depends="clean">
+        <delete file="${arxivTarFile}"/>
+        <delete file="${arxivTarFile}.gz"/>
+        <tar destfile="${arxivTarFile}" basedir="." includes="**"
+            excludes="*.dvi,*.ps,*.pdf,*.png,${arxivTarFile},${arxivTarFile}.gz,sandbox.*,bibliography/**,papers/**,talks/**,diagrams/pdf/**,diagrams/latex2pdf/**,diagrams/*"
+        />
+        <gzip src="${arxivTarFile}" destfile="${arxivTarFile}.gz"/>
+        <delete file="${arxivTarFile}"/>
+    </target>
+
+    <target name="bbl" depends="init">
+        <exec executable="latex">
+            <arg value="su_3-functoriality"/>
+        </exec>
+        <exec executable="bibtex">
+            <arg value="su_3-functoriality"/>
+        </exec>
+    </target>
+     
+    <target name="dvi" depends="bbl">
+        <exec executable="latex">
+            <arg value="su_3-functoriality"/>
+        </exec>
+        <exec executable="latex">
+            <arg value="su_3-functoriality"/>
+        </exec>
+    </target>
+
+    <target name="ps" depends="dvi">
+        <exec executable="dvips">
+            <arg value="su_3-functoriality"/>
+        </exec>
+    </target>
+
+    <target name="pdf" depends="ps">
+        <exec executable="ps2pdf">
+            <arg value="su_3-functoriality.ps"/>
+        </exec>
+    </target>
+    
+    <target name="eps-diagrams">
+        <exec executable="bash" dir="diagrams/scripts/">
+            <arg value="find_all_diagrams.sh"/>
+        </exec>
+        <exec executable="bash" dir="diagrams/scripts/">
+            <arg value="stripall.sh"/>
+        </exec>
+    </target>
+    
+    <target name="scott-copy-pdf" depends="pdf">
+        <copy file="su_3-foams.pdf" tofile="../../../../hosts/math.berkeley.edu/public_html/papers/su_3-functoriality.pdf"/>
+        <svn>
+            <commit dir="../../../../hosts/math.berkeley.edu/public_html/papers/"/>
+        </svn>
+    </target>
+
+</project>

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/latex2pdf/README.txt	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,3 @@
+*Create defontify.tex containing the latex you want.
+*Run defontify.bat.
+*Open nofonts.ps in Illustrator, and copy the pieces you want over to the .pdf you're working on.

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/latex2pdf/defontify.bat	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,4 @@
+latex defontify
+dvips -R0 defontify
+ps2pdf defontify.ps
+gs -r9600 -sDEVICE=pswrite -dNOCACHE -sOutputFile=nofonts.ps -q -dbatch -dNOPAUSE defontify.pdf -c quit

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/latex2pdf/defontify.tex	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,15 @@
+\documentclass{amsart}
+
+\newcommand{\pathtotrunk}{../../}
+% \input{\pathtotrunk text/article_preamble.tex}
+
+\pagestyle{empty}
+
+\begin{document}
+\thispagestyle{empty}
+
+\begin{align*}
+abc bca cab ab bc ca a b c \\
+x y z A u_x u_y u_z
+\end{align*}
+\end{document}

Binary file diagrams/pdf/barycentric/Ax.pdf has changed

Binary file diagrams/pdf/barycentric/Ay.pdf has changed

Binary file diagrams/pdf/barycentric/barycentric.pdf has changed

Binary file diagrams/pdf/barycentric/ux.pdf has changed

Binary file diagrams/pdf/barycentric/ux_c-a.pdf has changed

Binary file diagrams/pdf/barycentric/ux_ca.pdf has changed

Binary file diagrams/pdf/barycentric/uy.pdf has changed

Binary file diagrams/pdf/barycentric/uy_ca-b.pdf has changed

Binary file diagrams/pdf/barycentric/uy_cab.pdf has changed

Binary file diagrams/pdf/barycentric/uz.pdf has changed

Binary file diagrams/pdf/barycentric/uz_c-a-b.pdf has changed

Binary file diagrams/pdf/barycentric/uz_cab.pdf has changed

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/scripts/README.txt	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,11 @@
+The scripts in this directory automatically build .eps files out of .pdf
+files. You can ignore it if you're using pdflatex.
+
+find_all_diagrams attempts to determine which diagrams are being
+used, and creates the file diagrams.list
+
+stripall creates small .eps files from the .pdf files named in
+diagrams.list and extra_diagrams.list
+
+If find_all_diagrams isn't finding everything you need, add things
+by hand to extra_diagrams.list

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/scripts/diagrams.list	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,22 @@
+quasitriangular
+kauffmanbracket
+biggerbraiding
+SampleTangle
+RemovingSpaghettiO
+TraceTangle
+Multiplication
+TL3
+TLExample
+Eis
+AnnularConsequences
+TwoRs
+TwoRsInTL
+TwoRs
+TwoRs
+TwoRs
+TwoRsInTL
+TwoRsInTL
+TwoRsInTL
+SampleTangle
+translation/rectangular
+translation/composition

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/scripts/extra_diagrams.list	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,1 @@
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/scripts/find_all_diagrams.bat	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,1 @@
+bash find_all_diagrams.sh

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/scripts/find_all_diagrams.sh	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,9 @@
+rm diagrams.list
+for source in `ls ../../text/*.tex`;
+    do
+        ./find_diagrams.sh $source
+done;
+./find_diagrams.sh ../../sandbox.tex
+./find_diagrams.sh ../../todolist.tex
+./find_diagrams.sh ../latex2pdf/defontify.tex
+cat diagrams.list

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/scripts/find_diagrams.sh	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,3 @@
+grep -o '\\\mathfig{[0-9\. ]*}{[a-zA-z0-9\/_-]*}' $1 | sed -e 's/\\\mathfig{.*{\(.*\)/\1/' | sed -e 's/}//g' >> diagrams.list
+grep -o '\\\placefig{[0-9\. ]*}{[a-zA-z0-9\/_-]*}' $1 | sed -e 's/\\\placefig{.*{\(.*\)/\1/' | sed -e 's/}//g' >> diagrams.list
+grep -o '\\\rotatemathfig{ [0-9\.]*}{[0-9\.-]*}{[a-zA-z0-9\/_-]*}' $1 | sed -e 's/\\\rotatemathfig{.*{\(.*\)/\1/' | sed -e 's/}//g' >> diagrams.list

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/scripts/stripall.bat	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,1 @@
+bash stripall.sh

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/scripts/stripall.sh	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,19 @@
+for diagram in `cat diagrams.list`;
+    do
+        if [ ../pdf/$diagram.pdf -nt ../eps/$diagram.eps ]; then
+            echo "*** stripping $diagram";
+            ./strippdf.sh $diagram;
+        else
+            echo "$diagram is up to date"
+        fi
+done;
+dos2unix extra_diagrams.list
+for diagram in `cat extra_diagrams.list`;
+    do
+        if [ ../pdf/$diagram.pdf -nt ../eps/$diagram.eps ]; then
+            echo "*** stripping $diagram";
+            ./strippdf.sh $diagram;
+        else
+            echo "$diagram is up to date"
+        fi
+done;

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diagrams/scripts/strippdf.sh	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,4 @@
+gs -r2400 -dBATCH -dNOPAUSE -dSAFER -q -dNOCACHE -sDEVICE=epswrite -sOutputFile=temp1.eps ../pdf/$1.pdf
+sed -e '/CreationDate/d' temp1.eps > temp2.eps
+rm temp1.eps
+mv temp2.eps ../eps/$1.eps

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/preamble.tex	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,189 @@
+%auto-ignore
+%this ensures the arxiv doesn't try to start TeXing here.
+
+\usepackage{amsmath,amssymb,amsfonts}
+\usepackage{ifpdf}
+
+%\ifpdf
+%\usepackage[pdftex,all,color]{xy}
+%\else
+\usepackage[all,color]{xy}
+%\fi
+
+\SelectTips{cm}{}
+% This may speed up compilation of complex documents with many xymatrices.
+%\CompileMatrices
+
+% ----------------------------------------------------------------
+\vfuzz2pt % Don't report over-full v-boxes if over-edge is small
+\hfuzz2pt % Don't report over-full h-boxes if over-edge is small
+% ----------------------------------------------------------------
+
+% diagrams -------------------------------------------------------
+% figures ---------------------------------------------------------
+%%% borrowed from Dror's cobordisms paper, use this to include eps or pdf graphics.
+\ifpdf
+\newcommand{\pathtodiagrams}{\pathtotrunk diagrams/pdf/}
+\else
+\newcommand{\pathtodiagrams}{\pathtotrunk diagrams/eps/}
+\fi
+
+\newcommand{\mathfig}[2]{{\hspace{-3pt}\begin{array}{c}%
+  \raisebox{-2.5pt}{\includegraphics[width=#1\textwidth]{\pathtodiagrams #2}}%
+\end{array}\hspace{-3pt}}}
+\newcommand{\reflectmathfig}[2]{{\hspace{-3pt}\begin{array}{c}%
+  \raisebox{-2.5pt}{\reflectbox{\includegraphics[width=#1\textwidth]{\pathtodiagrams #2}}}%
+\end{array}\hspace{-3pt}}}
+\newcommand{\rotatemathfig}[3]{{\hspace{-3pt}\begin{array}{c}%
+  \raisebox{-2.5pt}{\rotatebox{#2}{\includegraphics[height=#1\textwidth]{\pathtodiagrams #3}}}%
+\end{array}\hspace{-3pt}}}
+\newcommand{\placefig}[2]{\includegraphics[width=#1\linewidth]{\pathtodiagrams #2}}
+
+\ifpdf
+\usepackage[pdftex,plainpages=false,hypertexnames=false,pdfpagelabels]{hyperref}
+\else
+\usepackage[dvips,plainpages=false,hypertexnames=false]{hyperref}
+\fi
+\newcommand{\arxiv}[1]{\href{http://arxiv.org/abs/#1}{\tt arXiv:\nolinkurl{#1}}}
+\newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{{\tt DOI:#1}}}
+\newcommand{\mathscinet}[1]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{\tt #1}}
+
+
+% THEOREMS -------------------------------------------------------
+\theoremstyle{plain}
+\newtheorem*{fact}{Fact}
+\newtheorem{prop}{Proposition}[section]
+\newtheorem{conj}[prop]{Conjecture}
+\newtheorem{thm}[prop]{Theorem}
+\newtheorem{lem}[prop]{Lemma}
+\newtheorem{lemma}[prop]{Lemma}
+\newtheorem{cor}[prop]{Corollary}
+\newtheorem*{cor*}{Corollary}
+\newtheorem*{exc}{Exercise}
+%\theoremstyle{definition}
+\newtheorem{defn}[prop]{Definition}         % numbered definition
+\newtheorem*{defn*}{Definition}             % unnumbered definition
+\newtheorem{question}{Question}
+\newenvironment{rem}{\noindent\textsl{Remark.}}{}  % perhaps looks better than rem above?
+\numberwithin{equation}{section}
+%\numberwithin{figure}{section}
+
+% Marginal notes in draft mode -----------------------------------
+\newcommand{\scott}[1]{\stepcounter{comment}{{\color{blue} $\star^{(\arabic{comment})}$}}\marginpar{\color{blue}  $\star^{(\arabic{comment})}$ \usefont{T1}{scott}{m}{n}  #1 --S}}     % draft mode
+\newcommand{\ari}[1]{\stepcounter{comment}{\color{red} $\star^{(\arabic{comment})}$}\marginpar{\color{red}  $\star^{(\arabic{comment})}$  #1 --A}}     % draft mode
+\newcommand{\comment}[1]{\stepcounter{comment}$\star^{(\arabic{comment})}$\marginpar{\tiny $\star^{(\arabic{comment})}$ #1}}     % draft mode
+\newcounter{comment}
+\newcommand{\noop}[1]{}
+\newcommand{\todo}[1]{\textbf{TODO: #1}}
+
+% \mathrlap -- a horizontal \smash--------------------------------
+% For comparison, the existing overlap macros:
+% \def\llap#1{\hbox to 0pt{\hss#1}}
+% \def\rlap#1{\hbox to 0pt{#1\hss}}
+\def\clap#1{\hbox to 0pt{\hss#1\hss}}
+\def\mathllap{\mathpalette\mathllapinternal}
+\def\mathrlap{\mathpalette\mathrlapinternal}
+\def\mathclap{\mathpalette\mathclapinternal}
+\def\mathllapinternal#1#2{%
+\llap{$\mathsurround=0pt#1{#2}$}}
+\def\mathrlapinternal#1#2{%
+\rlap{$\mathsurround=0pt#1{#2}$}}
+\def\mathclapinternal#1#2{%
+\clap{$\mathsurround=0pt#1{#2}$}}
+
+% MATH -----------------------------------------------------------
+\newcommand{\Natural}{\mathbb N}
+\newcommand{\Integer}{\mathbb Z}
+\newcommand{\Rational}{\mathbb Q}
+\newcommand{\Real}{\mathbb R}
+\newcommand{\Complex}{\mathbb C}
+\newcommand{\Field}{\mathbb F}
+
+\newcommand{\Id}{\boldsymbol{1}}
+\renewcommand{\imath}{\mathfrak{i}}
+\renewcommand{\jmath}{\mathfrak{j}}
+
+\newcommand{\qRing}{\Integer[q,q^{-1}]}
+\newcommand{\qMod}{\qRing-\operatorname{Mod}}
+\newcommand{\ZMod}{\Integer-\operatorname{Mod}}
+
+\newcommand{\To}{\rightarrow}
+\newcommand{\Into}{\hookrightarrow}
+\newcommand{\Onto}{\mapsto}
+\newcommand{\Iso}{\cong}
+\newcommand{\ActsOn}{\circlearrowright}
+
+\newcommand{\htpy}{\simeq}
+
+\newcommand{\restrict}[2]{#1{}_{\mid #2}{}}
+\newcommand{\set}[1]{\left\{#1\right\}}
+\newcommand{\setc}[2]{\left\{#1 \;\left| \; #2 \right. \right\}}
+\newcommand{\relations}[2]{\left<#1 \;\left| \; #2 \right. \right>}
+\newcommand{\cone}[3]{C\left(#1 \xrightarrow{#2} #3\right)}
+\newcommand{\pairing}[2]{\left\langle#1 ,#2 \right\rangle}
+
+\newcommand{\card}[1]{\sharp{#1}}
+
+\newcommand{\bdy}{\partial}
+\newcommand{\compose}{\circ}
+\newcommand{\eset}{\emptyset}
+
+\newcommand{\Cat}{\mathcal{C}}
+
+\newcommand{\psmallmatrix}[1]{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)}
+
+\newcommand{\qiq}[2]{[#1]_{#2}}
+\newcommand{\qi}[1]{\qiq{#1}{q}}
+\newcommand{\qdim}{\operatorname{dim_q}}
+
+\newcommand{\directSum}{\oplus}
+\newcommand{\DirectSum}{\bigoplus}
+\newcommand{\tensor}{\otimes}
+\newcommand{\Tensor}{\bigotimes}
+
+\newcommand{\db}[1]{\left(\left(#1\right)\right)}
+
+\newcommand{\su}[1]{\mathfrak{su}_{#1}}
+\newcommand{\csl}[1]{\mathfrak{sl}_{#1}}
+\newcommand{\uqsl}[1]{U_q\left(\csl{#1}\right)}
+
+\newcommand{\Cobl}{{\mathcal Cob}_{/l}}
+\newcommand{\Cob}[1]{{\mathcal Cob}\left(\su{#1}\right)}
+\newcommand{\Kom}[1]{\operatorname{Kom}\left(#1\right)}
+
+\newcommand{\Mat}[1]{\mathbf{Mat}\left(#1\right)}
+\newcommand{\Kar}[1]{\mathbf{Kar}\left(#1\right)}
+\newcommand{\Inv}[1]{\operatorname{Inv}\left(#1\right)}
+\newcommand{\Hom}[3]{\operatorname{Hom}_{#1}\left(#2,#3\right)}
+\newcommand{\End}[1]{\operatorname{End}\left(#1\right)}
+
+\newcommand{\Gr}[2]{\text{Gr}(#1 \subset #2)}
+\newcommand{\Flag}[3]{\text{Flag}(#1 \subset #2 \subset #3)}
+
+\def\llbracket{\left[\!\!\left[}
+\def\rrbracket{\right]\!\!\right]}
+\newcommand{\Kh}[1]{\llbracket#1\rrbracket}
+\newcommand{\mirror}[1]{\overline{#1}}%
+
+\newcommand{\Tangles}{{\mathbf{Oriented Tangles}}}
+\newcommand{\Spider}[1]{{\mathbf{Spider}\left(#1\right)}}
+\newcommand{\TL}{\mathcal{TL}}
+\newcommand{\Foam}[1]{\mathbf{Foam}\left(#1\right)}
+
+\newcommand{\directSumStack}[2]{{\begin{matrix}#1 \\ \DirectSum \\#2\end{matrix}}}
+\newcommand{\directSumStackThree}[3]{{\begin{matrix}#1 \\ \DirectSum \\#2 \\ \DirectSum \\#3\end{matrix}}}
+
+\newcommand{\grading}[1]{{\color{blue}\{#1\}}}
+\newcommand{\shift}[1]{\left[#1\right]}
+
+\newenvironment{narrow}[2]{%
+\vspace{-0.4cm}% horrible hack, by scott % this only seems to be appropriate in beamer mode...
+\begin{list}{}{%
+\setlength{\topsep}{0pt}%
+\setlength{\leftmargin}{#1}%
+\setlength{\rightmargin}{#2}%
+\setlength{\listparindent}{\parindent}%
+\setlength{\itemindent}{\parindent}%
+\setlength{\parsep}{\parskip}}%
+\item[]}{\end{list}}
+% ----------------------------------------------------------------

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/text/article_preamble.tex	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,29 @@
+%auto-ignore
+%this ensures the arxiv doesn't try to start TeXing here.
+
+\input{\pathtotrunk preamble.tex}
+
+\usepackage{breakurl}
+
+\ifpdf
+\usepackage[pdftex]{graphicx}
+\else
+\usepackage[dvips]{graphicx}
+\fi
+
+\usepackage{color}
+
+% This switches fonts to the Palatino family.
+\renewcommand{\familydefault}{ppl}
+
+%%% futzing with margins following Dror (from Karoubi)
+%\marginparwidth 0pt%
+%\marginparsep 0pt
+
+\textwidth   5.5in%
+\textheight  9.0in%
+\oddsidemargin 12pt%
+\evensidemargin 12pt
+
+\topmargin -.6in%
+\headsep .5in

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/text/top_matter.tex	Thu Apr 24 02:56:34 2008 +0000
@@ -0,0 +1,22 @@
+\title{Blob Homology}
+
+\author{Scott~Morrison}
+\address{
+}%
+\email{scott@tqft.net} \urladdr{http://tqft.net/}
+
+\author{Kevin~Walker}
+\address{
+}%
+\email{kevin@canyon23.net} \urladdr{http://canyon23.net/}
+
+
+\date{
+  First edition: the mysterious future
+  This edition: \today.
+}
+
+%\primaryclass{57M25} \secondaryclass{57M27; 57Q45}
+%\keywords{
+
+%}