...
authorscott@6e1638ff-ae45-0410-89bd-df963105f760
Wed, 28 Oct 2009 21:41:53 +0000
changeset 145 b5c1a6aec50d
parent 144 48b246f6a7ad
child 146 08bbcf3ec4d2
...
bibliography/bibliography.bib
text/intro.tex
text/ncat.tex
--- a/bibliography/bibliography.bib	Wed Oct 28 21:18:55 2009 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,523 +0,0 @@
-@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}}
-
-%S! fix this citation!
-@article{morrison-walker,
-    AUTHOR = {David Clark and Scott Morrison and Kevin Walker},
-    TITLE = {Fixing the functoriality of Khovanov homology},
-     note = {\arxiv{math.GT/0701339}},
-}
-
-@misc{kw:tqft,
-    AUTHOR = {Walker, Kevin},
-    TITLE  = {Topological Quantum Field Theories},
-    note    = {draft available at \url{http://canyon23.net/math/tc.pdf}},
-}
-
-@article {MR1854636,
-    AUTHOR = {Keller, Bernhard},
-     TITLE = {Introduction to {$A$}-infinity algebras and modules},
-   JOURNAL = {Homology Homotopy Appl.},
-  FJOURNAL = {Homology, Homotopy and Applications},
-    VOLUME = {3},
-      YEAR = {2001},
-    NUMBER = {1},
-     PAGES = {1--35 (electronic)},
-      ISSN = {1512-0139},
-   MRCLASS = {18E30 (18D50 18G40 55P43 55U35)},
-  MRNUMBER = {MR1854636 (2004a:18008a)},
-MRREVIEWER = {Ulrike Tillmann},
-      note = {\mathscinet{MR1854636} \arxiv{math.RA/9910179}},
-}
-
-@incollection {MR2061854,
-    AUTHOR = {McClure, James E. and Smith, Jeffrey H.},
-     TITLE = {Operads and cosimplicial objects: an introduction},
- BOOKTITLE = {Axiomatic, enriched and motivic homotopy theory},
-    SERIES = {NATO Sci. Ser. II Math. Phys. Chem.},
-    VOLUME = {131},
-     PAGES = {133--171},
- PUBLISHER = {Kluwer Acad. Publ.},
-   ADDRESS = {Dordrecht},
-      YEAR = {2004},
-   MRCLASS = {55P48 (18D50)},
-  MRNUMBER = {MR2061854 (2005b:55018)},
-MRREVIEWER = {David Chataur},
-      note = {\mathscinet{MR2061854} \arxiv{math.QA/0402117}},
-}
-
-@book {MR0420610,
-    AUTHOR = {May, J. P.},
-     TITLE = {The geometry of iterated loop spaces},
- PUBLISHER = {Springer-Verlag},
-   ADDRESS = {Berlin},
-      YEAR = {1972},
-     PAGES = {viii+175},
-   MRCLASS = {55D35},
-  MRNUMBER = {MR0420610 (54 \#8623b)},
-MRREVIEWER = {J. Stasheff},
-      note = {Lectures Notes in Mathematics, Vol. 271 \mathscinet{MR0420610} \href{http://www.math.uchicago.edu/~may/BOOKS/gils.pdf}{available online}},
-}
-
-@article {MR0236922,
-    AUTHOR = {Boardman, J. M. and Vogt, R. M.},
-     TITLE = {Homotopy-everything {$H$}-spaces},
-   JOURNAL = {Bull. Amer. Math. Soc.},
-  FJOURNAL = {Bulletin of the American Mathematical Society},
-    VOLUME = {74},
-      YEAR = {1968},
-     PAGES = {1117--1122},
-      ISSN = {0002-9904},
-   MRCLASS = {55.42},
-  MRNUMBER = {MR0236922 (38 \#5215)},
-MRREVIEWER = {R. J. Milgram},
-      note = {\mathscinet{MR0236922} \doi{10.1090/S0002-9904-1968-12070-1}},
-}
-
-@book {MR0420609,
-    AUTHOR = {Boardman, J. M. and Vogt, R. M.},
-     TITLE = {Homotopy invariant algebraic structures on topological spaces},
-    SERIES = {Lecture Notes in Mathematics, Vol. 347},
- PUBLISHER = {Springer-Verlag},
-   ADDRESS = {Berlin},
-      YEAR = {1973},
-     PAGES = {x+257},
-   MRCLASS = {55D35},
-  MRNUMBER = {MR0420609 (54 \#8623a)},
-MRREVIEWER = {J. Stasheff},
-      note = {\mathscinet{MR0420609}},
-}
-
-%The framed little discs operad:
-@article {MR1256989,
-    AUTHOR = {Getzler, E.},
-     TITLE = {Batalin-{V}ilkovisky algebras and two-dimensional topological
-              field theories},
-   JOURNAL = {Comm. Math. Phys.},
-  FJOURNAL = {Communications in Mathematical Physics},
-    VOLUME = {159},
-      YEAR = {1994},
-    NUMBER = {2},
-     PAGES = {265--285},
-      ISSN = {0010-3616},
-     CODEN = {CMPHAY},
-   MRCLASS = {81T70 (17B81 55Q99 58Z05 81T40)},
-  MRNUMBER = {MR1256989 (95h:81099)},
-MRREVIEWER = {J. Stasheff},
-      note = {\mathscinet{MR1256989} \euclid{1104254599}},
-}
-
-
-
-
-
-@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}},
-}
-
-
-@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)},
-}
-
-@article {MR1624157,
-    AUTHOR = {Bullock, Doug and Frohman, Charles and Kania-Bartoszy{\'n}ska,
-              Joanna},
-     TITLE = {Skein homology},
-   JOURNAL = {Canad. Math. Bull.},
-  FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de
-              Math\'ematiques},
-    VOLUME = {41},
-      YEAR = {1998},
-    NUMBER = {2},
-     PAGES = {140--144},
-      ISSN = {0008-4395},
-     CODEN = {CMBUA3},
-   MRCLASS = {57M25 (55N35)},
-  MRNUMBER = {MR1624157 (99g:57006)},
-MRREVIEWER = {Daniel Ruberman},
- note = {\arxiv{q-alg/9701019} \mathscinet{MR1624157}},
-}
-	
--- a/text/intro.tex	Wed Oct 28 21:18:55 2009 +0000
+++ b/text/intro.tex	Wed Oct 28 21:41:53 2009 +0000
@@ -207,7 +207,7 @@
 
 
 
-\begin{property}[Relation to mapping spaces]
+\begin{property}[Mapping spaces]
 Let $\pi^\infty_{\le n}(W)$ denote the $A_\infty$ $n$-category based on maps 
 $B^n \to W$.
 (The case $n=1$ is the usual $A_\infty$ category of paths in $W$.)
--- a/text/ncat.tex	Wed Oct 28 21:18:55 2009 +0000
+++ b/text/ncat.tex	Wed Oct 28 21:41:53 2009 +0000
@@ -39,7 +39,7 @@
 a separate set of 2-morphisms for each rectangle $[0,l_1]\times [0,l_2] \sub \r^2$,
 and so on.
 (This allows for strict associativity.)
-Still other definitions \nn{need refs for all these; maybe the Leinster book}
+Still other definitions \nn{need refs for all these; maybe the Leinster book \cite{MR2094071}}
 model the $k$-morphisms on more complicated combinatorial polyhedra.
 
 We will allow our $k$-morphisms to have any shape, so long as it is homeomorphic to