writing definitions of topological a_\infty categories, modules, etc.
--- a/bibliography/bibliography.bib Tue Jul 01 01:53:15 2008 +0000
+++ b/bibliography/bibliography.bib Tue Jul 01 04:00:22 2008 +0000
@@ -7,6 +7,19 @@
@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 {MR1917056,
AUTHOR = {Bar-Natan, Dror},
TITLE = {On {K}hovanov's categorification of the {J}ones polynomial},
@@ -352,18 +365,6 @@
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}},
--- a/blob1.tex Tue Jul 01 01:53:15 2008 +0000
+++ b/blob1.tex Tue Jul 01 04:00:22 2008 +0000
@@ -229,7 +229,7 @@
\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).
+These functors must satisfy various properties (see \cite{kw:tqft} for details).
For example:
there is a canonical identification $\cC(X \du Y) = \cC(X) \times \cC(Y)$;
there is a restriction map $\cC(X) \to \cC(\bd X)$;
@@ -381,7 +381,7 @@
\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 $B^n$).
-See KW TQFT notes for details. Need to transfer details to here.}
+See \cite{kw:tqft} for details. Need to transfer details to here.}
For maps into spaces, $U(B^n; c)$ is generated by things of the form $a-b \in \cC_l(B^n; c)$,
where $a$ and $b$ are maps (fields) which are homotopic rel boundary.
@@ -403,7 +403,7 @@
the $n$-manifold $Y$ modulo local relations.
The Hilbert space $Z(Y; c)$ for the TQFT based on the fields and local relations
is defined to be the dual of $A(Y; c)$.
-(See KW TQFT notes or xxxx for details.)
+(See \cite{kw:tqft} or xxxx for details.)
The blob complex is in some sense the derived version of $A(Y; c)$.
@@ -918,15 +918,111 @@
\subsection{`Topological' $A_\infty$ $n$-categories}
\label{sec:topological-A-infty}%
-This section prepares the ground for establishing Property \ref{property:gluing} by defining the notion of a \emph{topological $A_\infty$
-$n$-category}. The main result of this section is
+This section prepares the ground for establishing Property \ref{property:gluing} by defining the notion of a \emph{topological $A_\infty$-$n$-category}.
+The main result of this section is
\begin{thm}
-Topological $A_\infty$ $1$-categories are equivalent to `standard'
-$A_\infty$ $1$-categories.
+Topological $A_\infty$-$1$-categories are equivalent to `standard'
+$A_\infty$-$1$-categories.
\end{thm}
+Before proving this theorem, we embark upon a long string of definitions. For expository purposes, we begin with the $n=1$ special cases, and define
+first topological $A_\infty$-algebras, then topological $A_\infty$-categories, and then topological $A_\infty$-modules over these. We then turn
+to the general $n$ case, defining topological $A_\infty$-$n$-categories and their modules.
+\nn{Something about duals?}
+\todo{Explain that we're not making contact with any previous notions for the general $n$ case?}
+\begin{defn}
+\label{defn:topological-algebra}%
+A ``topological $A_\infty$-algebra'' $A$ consists of the data
+\begin{enumerate}
+\item for each $1$-manifold $J$ diffeomorphic to the standard interval $I=\left[0,1\right]$, a complex of vector spaces $A(J)$,
+\item along with an `evaluation' chain map $\ev_J : \CD{J} \tensor A(J) \to A(J)$,
+\item for each diffeomorphism $\phi : J \to J'$, an isomorphism $A(\phi) : A(J) \isoto A(J')$,
+\item and whenever $\bdy J \cap \bdy J'$ is a single point, a gluing map $\gl_{J,J'} : A(J) \tensor A(J') \to A(J \cup J')$,
+\end{enumerate}
+satisfying the following conditions.
+\begin{itemize}
+\item If $\phi$ is a diffeomorphism from $J$ to itself, the maps $\ev_J(\phi, -)$ and $A(\phi)$ are the same.
+\item The evaluation chain map is associative, in that the diagram
+\begin{equation*}
+\xymatrix{
+\CD{J} \tensor \CD{J} \tensor A(J) \ar[r]^{\Id \tensor \ev_J} \ar[d]_{\compose \tensor \Id} &
+\CD{J} \tensor A(J) \ar[d]^{\ev_J} \\
+\CD{J} \tensor A(J) \ar[r]_{\ev_J} &
+A(J)
+}
+\end{equation*}
+commutes. (Here the map $\compose : \CD{J} \tensor \CD{J} \to \CD{J}$ is a composition: take products of singular chains first, then use the group multiplication in $\Diff(J)$.)
+\item The gluing maps are \emph{strictly} associative. That is, given $J$, $J'$ and $J''$, the diagram
+\begin{equation*}
+\xymatrix{
+A(J) \tensor A(J') \tensor A(J'') \ar[rr]^{\gl_{J,J'} \tensor \Id} \ar[d]_{\Id \tensor \gl_{J',J''}} &&
+A(J \cup J') \tensor A(J'') \ar[d]^{\gl_{J \cup J', J''}} \\
+A(J) \tensor A(J' \cup J'') \ar[rr]_{\gl_{J, J' \cup J''}} &&
+A(J \cup J' \cup J'')
+}
+\end{equation*}
+commutes.
+\end{itemize}
+\end{defn}
+
+\begin{rem}
+Of course, the first and third pieces of data (the complexes, and the isomorphisms) together just constitute a functor from the category of
+intervals and diffeomorphisms between them to the category of complexes of vector spaces.
+Further, one can combine the second and third pieces of data, asking instead for a map
+\begin{equation*}
+\ev_{J,J'} : \CD{J \to J'} \tensor A(J) \to A(J').
+\end{equation*}
+(Any $k$-parameter family of diffeomorphisms in $C_k(\Diff(J \to J'))$ factors into a single diffeomorphism $J \to J'$ and a $k$-parameter family of
+diffeomorphisms in $\CD{J'}$.)
+\end{rem}
+
+To generalise the definition to that of a category, we simply introduce a set of objects which we call $A(pt)$. Now we associate complexes to each
+interval with boundary conditions $(J, c_-, c_+)$, with $c_-, c_+ \in A(pt)$, and only ask for gluing maps when the boundary conditions match up:
+\begin{equation*}
+\gl : A(J, c_-, c_0) \tensor A(J', c_0, c_+) \to A(J \cup J', c_-, c_+).
+\end{equation*}
+The action of diffeomorphisms, and $k$-parameter families of diffeomorphisms, ignore the boundary conditions.
+
+The definition of a module follows closely the definition of an algebra or category.
+\begin{defn}
+\label{defn:topological-module}%
+A topological $A_\infty$-(left-)module $M$ over a topological $A_\infty$ category $A$ consists of the data
+\begin{enumerate}
+\item a functor $K \mapsto M(K)$ from $1$-manifolds diffeomorphic to the standard interval, with a marked point on a boundary, to complexes of vector spaces,
+\item along with an `evaluation' map $\ev_K : \CD{K} \tensor M(K) \to M(K)$
+\item whenever $\bdy J \cap K$ is a single point, and isn't the marked point of $K$ \todo{ugh, that's so gross}, a gluing map
+$\gl_{J,K} : A(J) \tensor M(K) \to M(J \cup K)$
+\end{enumerate}
+satisfying the obvious analogous conditions as in Definition \ref{defn:topological-algebra}.
+\end{defn}
+
+\todo{Bimodules, and gluing}
+
+\todo{the motivating example $C_*(\maps(X, M))$}
+
+\todo{higher $n$}
+
+
+\newcommand{\skel}[1]{\operatorname{skeleton}(#1)}
+
+Given a topological $A_\infty$-category $\cC$, we can construct an `algebraic' $A_\infty$ category $\skel{\cC}$. First, pick your
+favorite diffeomorphism $\phi: I \cup I \to I$.
+\begin{defn}
+We'll write $\skel{\cC} = (A, m_k)$. Define $A = \cC(I)$, and $m_2 : A \tensor A \to A$ by
+\begin{equation*}
+m_2 \cC(I) \tensor \cC(I) \xrightarrow{\gl_{I,I}} \cC(I \cup I) \xrightarrow{\cC(\phi)} \cC(I).
+\end{equation*}
+Next, we define all the `higher associators' $m_k$ by
+\todo{}
+\end{defn}
+
+Give an `algebraic' $A_\infty$ category $(A, m_k)$, we can construct a topological $A_\infty$-category, which we call $\bc_*^A$. You should
+think of this at the generalisation of the blob complex, although the construction we give will \emph{not} specialise to exactly the usual definition
+in the case the $A$ is actually an associative category.
+\begin{defn}
+\end{defn}
\nn{Need to let the input $n$-category $C$ be a graded thing (e.g. DG
$n$-category or $A_\infty$ $n$-category). DG $n$-category case is pretty
@@ -1196,8 +1292,8 @@
\input{text/explicit.tex}
% ----------------------------------------------------------------
-\newcommand{\urlprefix}{}
-\bibliographystyle{gtart}
+%\newcommand{\urlprefix}{}
+\bibliographystyle{plain}
%Included for winedt:
%input "bibliography/bibliography.bib"
\bibliography{bibliography/bibliography}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/gtart.bst Tue Jul 01 04:00:22 2008 +0000
@@ -0,0 +1,1340 @@
+%%
+%% This is file `gtart.bst',
+%% generated with the docstrip utility.
+%%
+%%
+%% The original source files were:
+%%
+%% merlin.mbs (with options: `ed-au,nmft,nmft-bf,dt-jnl,yr-par,xmth,yrp-x,tit-it,atit-u,jttl-rm,vnum-x,volp-blk,jdt-vs,pp-last,num-xser,numser,jnm-x,bkpg-x,pre-edn,edpar,edby-par,edbyy,blk-com,in-x,fin-bare,ppx,xedn,and-xcom,xand,eprint,url,url-blk,nfss')
+%% ----------------------------------------
+%% *** For Geometry and Topology Publications ***
+%%
+%% Copyright 1994-1999 Patrick W Daly
+%%
+%% Modified by Boris Okun 12/2001
+%%
+ % ===============================================================
+ % IMPORTANT NOTICE:
+ % This bibliographic style (bst) file has been generated from one or
+ % more master bibliographic style (mbs) files, listed above.
+ %
+ % This generated file can be redistributed and/or modified under the terms
+ % of the LaTeX Project Public License Distributed from CTAN
+ % archives in directory macros/latex/base/lppl.txt; either
+ % version 1 of the License, or any later version.
+ % ===============================================================
+ % Name and version information of the main mbs file:
+ % \ProvidesFile{merlin.mbs}[1999/03/18 3.88 (PWD)]
+ % For use with BibTeX version 0.99a or later
+ %-------------------------------------------------------------------
+ % This bibliography style file is intended for texts in ENGLISH
+ % This is a numerical citation style, and as such is standard LaTeX.
+ % It requires no extra package to interface to the main text.
+ % The form of the \bibitem entries is
+ % \bibitem{key}...
+ % Usage of \cite is as follows:
+ % \cite{key} ==>> [#]
+ % \cite[chap. 2]{key} ==>> [#, chap. 2]
+ % where # is a number determined by the ordering in the reference list.
+ % The order in the reference list is alphabetical by authors.
+ %---------------------------------------------------------------------
+
+ENTRY
+ { address
+ author
+ booktitle
+ chapter
+ edition
+ editor
+ howpublished
+ institution
+ journal
+ key
+ month
+ note
+ number
+ organization
+ pages
+ publisher
+ school
+ series
+ title
+ type
+ url
+ volume
+ year
+ }
+ {}
+ { label }
+
+INTEGERS { output.state before.all mid.sentence after.sentence after.block }
+
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+ #1 'mid.sentence :=
+ #2 'after.sentence :=
+ #3 'after.block :=
+}
+
+STRINGS { s t }
+
+FUNCTION {output.nonnull}
+{ 's :=
+ output.state mid.sentence =
+ { ", " * write$ }
+ { output.state after.block =
+ { add.period$ write$
+ newline$
+ "\newblock " write$
+ }
+ { output.state before.all =
+ 'write$
+ { add.period$ " " * write$ }
+ if$
+ }
+ if$
+ mid.sentence 'output.state :=
+ }
+ if$
+ s
+}
+
+FUNCTION {output}
+{ duplicate$ empty$
+ 'pop$
+ 'output.nonnull
+ if$
+}
+
+FUNCTION {output.check}
+{ 't :=
+ duplicate$ empty$
+ { pop$ "empty " t * " in " * cite$ * warning$ }
+ 'output.nonnull
+ if$
+}
+
+FUNCTION {fin.entry}
+{ duplicate$ empty$
+ 'pop$
+ 'write$
+ if$
+ newline$
+}
+
+FUNCTION {new.block}
+{ output.state before.all =
+ 'skip$
+ { after.block 'output.state := }
+ if$
+}
+
+FUNCTION {new.sentence}
+{ output.state after.block =
+ 'skip$
+ { output.state before.all =
+ 'skip$
+ { after.sentence 'output.state := }
+ if$
+ }
+ if$
+}
+
+FUNCTION {add.blank}
+{ " " * before.all 'output.state :=
+}
+
+FUNCTION {date.block}
+{
+ add.blank
+}
+
+FUNCTION {not}
+{ { #0 }
+ { #1 }
+ if$
+}
+
+FUNCTION {and}
+{ 'skip$
+ { pop$ #0 }
+ if$
+}
+
+FUNCTION {or}
+{ { pop$ #1 }
+ 'skip$
+ if$
+}
+
+FUNCTION {new.block.checka}
+{ empty$
+ 'skip$
+ 'new.block
+ if$
+}
+
+FUNCTION {new.block.checkb}
+{ empty$
+ swap$ empty$
+ and
+ 'skip$
+ 'new.block
+ if$
+}
+
+FUNCTION {new.sentence.checka}
+{ empty$
+ 'skip$
+ 'new.sentence
+ if$
+}
+
+FUNCTION {new.sentence.checkb}
+{ empty$
+ swap$ empty$
+ and
+ 'skip$
+ 'new.sentence
+ if$
+}
+
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+ { pop$ "" }
+ 'skip$
+ if$
+}
+
+FUNCTION {emphasize}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "\emph{" swap$ * "}" * }
+ if$
+}
+
+FUNCTION {bolden}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "\textbf{" swap$ * "}" * }
+ if$
+}
+
+FUNCTION {quotify}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "``" swap$ * "''" * }
+ if$
+}
+
+
+FUNCTION {bib.name.font}
+{ bolden }
+
+FUNCTION {bib.fname.font}
+{ bib.name.font }
+FUNCTION {capitalize}
+{ "u" change.case$ "t" change.case$ }
+
+FUNCTION {space.word}
+{ " " swap$ * " " * }
+
+ % Here are the language-specific definitions for explicit words.
+ % Each function has a name bbl.xxx where xxx is the English word.
+ % The language selected here is ENGLISH
+FUNCTION {bbl.and}
+{ "and"}
+
+FUNCTION {bbl.etal}
+{ "et~al." }
+
+FUNCTION {bbl.editors}
+{ "editors" }
+
+FUNCTION {bbl.editor}
+{ "editor" }
+
+FUNCTION {bbl.edby}
+{ "edited by" }
+
+FUNCTION {bbl.edition}
+{ "edition" }
+
+FUNCTION {bbl.volume}
+{ "volume" }
+
+FUNCTION {bbl.of}
+{ "of" }
+
+FUNCTION {bbl.number}
+{ "number" }
+
+FUNCTION {bbl.nr}
+{ "no." }
+
+FUNCTION {bbl.in}
+{ "in" }
+
+FUNCTION {bbl.pages}
+{ "" }
+
+FUNCTION {bbl.page}
+{ "" }
+
+FUNCTION {bbl.chapter}
+{ "chapter" }
+
+FUNCTION {bbl.techrep}
+{ "Technical Report" }
+
+FUNCTION {bbl.mthesis}
+{ "Master's thesis" }
+
+FUNCTION {bbl.phdthesis}
+{ "Ph.D. thesis" }
+
+MACRO {jan} {"January"}
+
+MACRO {feb} {"February"}
+
+MACRO {mar} {"March"}
+
+MACRO {apr} {"April"}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"June"}
+
+MACRO {jul} {"July"}
+
+MACRO {aug} {"August"}
+
+MACRO {sep} {"September"}
+
+MACRO {oct} {"October"}
+
+MACRO {nov} {"November"}
+
+MACRO {dec} {"December"}
+
+FUNCTION {format.url}
+{ url empty$
+ { "" }
+ { "\urlprefix\url{" url * "}" * }
+ if$
+}
+
+INTEGERS { nameptr namesleft numnames charptr}
+
+STRINGS {i j}
+
+FUNCTION {remove.periods}
+{'i :=
+ ""
+ #1 'charptr :=
+ " " 'j :=
+ {#1 j "" = - }
+ {i charptr #1 substring$
+ 'j :=
+ j "." =
+ {charptr #1 + 'charptr :=
+ i charptr #1 substring$
+ 'j :=
+ j "~" =
+ {"\," *}
+ {j *}
+ if$}
+ {j *}
+ if$
+ charptr #1 + 'charptr :=
+ }
+ while$
+}
+
+FUNCTION {format.names}
+{ 's :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ "{ff }{vv~}{ll}{, jj}" format.name$
+ remove.periods
+ 't :=
+ nameptr #1 >
+ {
+ namesleft #1 >
+ { ", " * t * }
+ {
+ "," *
+ s nameptr "{ll}" format.name$ duplicate$ "others" =
+ { 't := }
+ { pop$ }
+ if$
+ t "others" =
+ {
+ " " * bbl.etal *
+% bib.name.font
+ }
+ { " " * t * }
+ if$
+ }
+ if$
+ }
+ 't
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+% t "others" =
+% 'skip$
+% { bib.name.font }
+% if$
+}
+
+FUNCTION {bformat.names} % Formats names in bold, but keeps punctuation normal
+{ 's :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ "{ff }{vv~}{ll}{, jj}" format.name$
+ remove.periods
+ bib.name.font
+ 't :=
+ nameptr #1 >
+ {
+ namesleft #1 >
+ { ", " * t * }
+ {
+ "," *
+ s nameptr "{ll}" format.name$ duplicate$ "others" =
+ { 't := }
+ { pop$ }
+ if$
+ t "others" =
+ {
+ " " * bbl.etal *
+% bib.name.font
+ }
+ { " " * t * }
+ if$
+ }
+ if$
+ }
+ 't
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+% t "others" =
+% 'skip$
+% { bib.name.font }
+% if$
+}
+
+FUNCTION {format.names.ed}
+{ format.names }
+FUNCTION {format.authors}
+{ author empty$
+ { "" }
+ { author bformat.names }
+% bib.name.font}
+ if$
+}
+
+FUNCTION {format.editors}
+{ editor empty$
+ { "" }
+ { editor bformat.names
+% bib.name.font
+ editor num.names$ #1 >
+ { " (" * bbl.editors * ")" * }
+ { " (" * bbl.editor * ")" * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.in.editors}
+{ editor empty$
+ { "" }
+ { editor format.names.ed
+ }
+ if$
+}
+
+FUNCTION {format.note}
+{
+ note empty$
+ { "" }
+ { note #1 #1 substring$
+ duplicate$ "{" =
+ 'skip$
+ { output.state mid.sentence =
+ { "l" }
+ { "u" }
+ if$
+ change.case$
+ }
+ if$
+ note #2 global.max$ substring$ *
+ }
+ if$
+}
+
+FUNCTION {format.title}
+{ title empty$
+ { "" }
+ { title
+ emphasize
+ }
+ if$
+}
+
+FUNCTION {output.bibitem}
+{ newline$
+ "\bibitem{" write$
+ cite$ write$
+ "}" write$
+ newline$
+ ""
+ before.all 'output.state :=
+}
+
+FUNCTION {n.dashify}
+{
+ 't :=
+ ""
+ { t empty$ not }
+ { t #1 #1 substring$ "-" =
+ { t #1 #2 substring$ "--" = not
+ { "--" *
+ t #2 global.max$ substring$ 't :=
+ }
+ { { t #1 #1 substring$ "-" = }
+ { "-" *
+ t #2 global.max$ substring$ 't :=
+ }
+ while$
+ }
+ if$
+ }
+ { t #1 #1 substring$ *
+ t #2 global.max$ substring$ 't :=
+ }
+ if$
+ }
+ while$
+}
+
+FUNCTION {word.in}
+{ "from: " }
+
+FUNCTION {format.date}
+{ year empty$
+ { "" }
+ 'year
+ if$
+ duplicate$ empty$
+ 'skip$
+ {
+ before.all 'output.state :=
+ " (" swap$ * ")" *
+ }
+ if$
+}
+
+FUNCTION{format.year}
+{ year duplicate$ empty$
+ { "empty year in " cite$ * warning$ pop$ "" }
+ { " (" swap$ * ")" * }
+ if$
+}
+
+FUNCTION {format.btitle}
+{ title emphasize
+}
+
+FUNCTION {tie.or.space.connect}
+{ duplicate$ text.length$ #3 <
+ { "~" }
+ { " " }
+ if$
+ swap$ * *
+}
+
+FUNCTION {either.or.check}
+{ empty$
+ 'pop$
+ { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+ if$
+}
+
+FUNCTION {format.bvolume}
+{ volume empty$
+ { "" }
+ { bbl.volume volume tie.or.space.connect
+ series empty$
+ 'skip$
+ { bbl.of space.word * series emphasize * }
+ if$
+ "volume and number" number either.or.check
+ }
+ if$
+}
+
+FUNCTION {format.bvolume.in}
+{series empty$
+ 'format.bvolume
+ {volume empty$
+ {""}
+ {series " " volume * *
+ "volume and number" number either.or.check }
+ if$
+ }
+if$
+}
+
+FUNCTION {format.number.series}
+{ volume empty$
+ { number empty$
+ { series field.or.null }
+ { series empty$
+ { number }
+ { output.state mid.sentence =
+ { bbl.number }
+ { bbl.number capitalize }
+ if$
+ number tie.or.space.connect
+ bbl.in space.word * series *
+ }
+ if$
+ }
+ if$
+ }
+ { "" }
+ if$
+}
+
+
+FUNCTION {format.number.series.in}
+{ volume empty$
+ {series empty$
+ 'format.number.series
+ {series
+ number empty$
+ 'skip$
+ {" " number * *}
+ if$ }
+ if$
+ }
+ { "" }
+if$
+}
+
+
+
+FUNCTION {format.edition}
+{ edition empty$
+ { "" }
+ { output.state mid.sentence =
+ { edition "l" change.case$ " " * bbl.edition * }
+ { edition "t" change.case$ " " * bbl.edition * }
+ if$
+ }
+ if$
+}
+
+INTEGERS { multiresult }
+
+FUNCTION {multi.page.check}
+{ 't :=
+ #0 'multiresult :=
+ { multiresult not
+ t empty$ not
+ and
+ }
+ { t #1 #1 substring$
+ duplicate$ "-" =
+ swap$ duplicate$ "," =
+ swap$ "+" =
+ or or
+ { #1 'multiresult := }
+ { t #2 global.max$ substring$ 't := }
+ if$
+ }
+ while$
+ multiresult
+}
+
+FUNCTION {format.pages}
+{ pages empty$
+ { "" }
+ { pages multi.page.check
+ { pages n.dashify }
+ { pages }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.journal.pages}
+{ pages empty$
+ 'skip$
+ { duplicate$ empty$
+ { pop$ format.pages }
+ {
+ " " *
+ pages n.dashify *
+ }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.vol.num.pages}
+{ volume field.or.null
+ format.year *
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+ { "" }
+ { type empty$
+ { bbl.chapter }
+ { type "l" change.case$ }
+ if$
+ chapter tie.or.space.connect
+ }
+ if$
+}
+
+FUNCTION {format.in.ed.booktitle}
+{ booktitle empty$
+ { "" }
+ { editor empty$
+ { word.in booktitle quotify * }
+ { word.in booktitle quotify *
+ ", (" *
+ format.in.editors *
+ ", " *
+ editor num.names$ #1 >
+ { bbl.editors }
+ { bbl.editor }
+ if$
+ *
+ ")" *
+ }
+ if$
+ }
+ if$
+}
+
+FUNCTION {empty.misc.check}
+{ author empty$ title empty$ howpublished empty$
+ month empty$ year empty$ note empty$
+ and and and and and
+ key empty$ not and
+ { "all relevant fields are empty in " cite$ * warning$ }
+ 'skip$
+ if$
+}
+
+FUNCTION {format.thesis.type}
+{ type empty$
+ 'skip$
+ { pop$
+ type "t" change.case$
+ }
+ if$
+}
+
+FUNCTION {format.tr.number}
+{ type empty$
+ { bbl.techrep }
+ 'type
+ if$
+ number empty$
+ { "t" change.case$ }
+ { number tie.or.space.connect }
+ if$
+}
+
+FUNCTION {format.article.crossref}
+{
+ key empty$
+ { journal empty$
+ { "need key or journal for " cite$ * " to crossref " * crossref *
+ warning$
+ ""
+ }
+ { word.in journal emphasize * }
+ if$
+ }
+ { word.in key * " " *}
+ if$
+ " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.crossref.editor}
+{ editor #1 "{vv~}{ll}" format.name$
+ editor num.names$ duplicate$
+ #2 >
+ { pop$
+ " " * bbl.etal *
+ }
+ { #2 <
+ 'skip$
+ { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+ {
+ " " * bbl.etal *
+ }
+ { bbl.and space.word * editor #2 "{vv~}{ll}" format.name$
+ * }
+ if$
+ }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.book.crossref}
+{ volume empty$
+ { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
+ word.in
+ }
+ { bbl.volume volume tie.or.space.connect
+ bbl.of space.word *
+ }
+ if$
+ editor empty$
+ editor field.or.null author field.or.null =
+ or
+ { key empty$
+ { series empty$
+ { "need editor, key, or series for " cite$ * " to crossref " *
+ crossref * warning$
+ "" *
+ }
+ { series emphasize * }
+ if$
+ }
+ { key * }
+ if$
+ }
+ { format.crossref.editor * }
+ if$
+ " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.incoll.inproc.crossref}
+{
+ editor empty$
+ editor field.or.null author field.or.null =
+ or
+ { key empty$
+ { booktitle empty$
+ { "need editor, key, or booktitle for " cite$ * " to crossref " *
+ crossref * warning$
+ ""
+ }
+ { word.in "``" booktitle "''" * * }
+ if$
+ }
+ { word.in key * " " *}
+ if$
+ }
+ { word.in format.crossref.editor * " " *}
+ if$
+ " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.org.or.pub}
+{ 't :=
+ ""
+ address empty$ t empty$ and
+ 'skip$
+ {
+ t empty$
+ { address empty$
+ 'skip$
+ { address * }
+ if$
+ }
+ { t *
+ address empty$
+ 'skip$
+ { ", " * address * }
+ if$
+ }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.publisher.address}
+{ publisher empty$
+ { "empty publisher in " cite$ * warning$
+ ""
+ }
+ { publisher }
+ if$
+ format.org.or.pub
+}
+
+FUNCTION {format.organization.address}
+{ organization empty$
+ { "" }
+ { organization }
+ if$
+ format.org.or.pub
+}
+
+FUNCTION {article}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { journal
+ "journal" output.check
+ add.blank
+ format.vol.num.pages output
+ }
+ { format.article.crossref output.nonnull
+% format.pages output
+ }
+ if$
+ format.journal.pages
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {book}
+{ output.bibitem
+ author empty$
+ { format.editors "author and editor" output.check
+ }
+ { format.authors output.nonnull
+ crossref missing$
+ { "author and editor" editor either.or.check }
+ 'skip$
+ if$
+ }
+ if$
+ format.btitle "title" output.check
+ crossref missing$
+ { format.bvolume output
+ format.edition output
+ format.number.series.in output
+ format.publisher.address output
+ }
+ {
+ format.book.crossref output.nonnull
+ }
+ if$
+ format.date "year" output.check
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {booklet}
+{ output.bibitem
+ format.authors output
+ format.title "title" output.check
+ howpublished output
+ address output
+ format.date output
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {incollection}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.in.ed.booktitle "booktitle" output.check
+ format.bvolume.in output
+ format.edition output
+ format.number.series.in output
+ format.publisher.address output
+ }
+ { format.incoll.inproc.crossref output.nonnull
+ }
+ if$
+ format.date "year" output.check
+ date.block
+ add.blank
+ format.pages "pages" output.check
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {inbook}{incollection}
+
+FUNCTION {inproceedings}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.in.ed.booktitle "booktitle" output.check
+ format.bvolume.in output
+ format.number.series.in output
+ publisher empty$
+ { format.organization.address output }
+ { organization output
+ format.publisher.address output
+ }
+ if$
+ }
+ { format.incoll.inproc.crossref output.nonnull
+ }
+ if$
+ format.date "year" output.check
+ date.block
+ add.blank
+ format.pages "pages" output.check
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {conference} { inproceedings }
+
+FUNCTION {manual}
+{ output.bibitem
+ author empty$
+ { organization empty$
+ 'skip$
+ { organization output.nonnull
+ address output
+ }
+ if$
+ }
+ { format.authors output.nonnull }
+ if$
+ format.btitle "title" output.check
+ author empty$
+ { organization empty$
+ {
+ address output
+ }
+ 'skip$
+ if$
+ }
+ {
+ organization output
+ address output
+ }
+ if$
+ format.edition output
+ format.date output
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {mastersthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ format.btitle "title" output.check
+ bbl.mthesis format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ format.date "year" output.check
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {misc}
+{ output.bibitem
+ format.authors output
+ format.title output
+ howpublished output
+ format.date output
+ format.url output
+ format.note output
+ fin.entry
+ empty.misc.check
+}
+
+FUNCTION {phdthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ format.btitle "title" output.check
+ bbl.phdthesis format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ format.date "year" output.check
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {proceedings}
+{ output.bibitem
+ editor empty$
+ { organization output }
+ { format.editors output.nonnull }
+ if$
+ format.btitle "title" output.check
+ format.bvolume output
+ editor empty$
+ { publisher empty$
+ 'skip$
+ {
+ format.number.series output
+ format.publisher.address output
+ }
+ if$
+ }
+ { publisher empty$
+ {
+ format.organization.address output }
+ {
+ organization output
+ format.publisher.address output
+ }
+ if$
+ }
+ if$
+ format.date "year" output.check
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {techreport}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ format.tr.number output.nonnull
+ institution "institution" output.check
+ address output
+ format.date "year" output.check
+ format.url output
+ format.note output
+ fin.entry
+}
+
+FUNCTION {unpublished}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ format.date output
+ format.url output
+ format.note "note" output.check
+ fin.entry
+}
+
+FUNCTION {default.type} { misc }
+
+READ
+
+FUNCTION {sortify}
+{ purify$
+ "l" change.case$
+}
+
+INTEGERS { len }
+
+FUNCTION {chop.word}
+{ 's :=
+ 'len :=
+ s #1 len substring$ =
+ { s len #1 + global.max$ substring$ }
+ 's
+ if$
+}
+
+FUNCTION {sort.format.names}
+{ 's :=
+ #1 'nameptr :=
+ ""
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ "{vv{ } }{ll{ }}{ ff{ }}{ jj{ }}"
+ format.name$ 't :=
+ nameptr #1 >
+ {
+ " " *
+ namesleft #1 = t "others" = and
+ { "zzzzz" * }
+ { t sortify * }
+ if$
+ }
+ { t sortify * }
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+}
+
+FUNCTION {sort.format.title}
+{ 't :=
+ "A " #2
+ "An " #3
+ "The " #4 t chop.word
+ chop.word
+ chop.word
+ sortify
+ #1 global.max$ substring$
+}
+
+FUNCTION {author.sort}
+{ author empty$
+ { key empty$
+ { "to sort, need author or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { author sort.format.names }
+ if$
+}
+
+FUNCTION {author.editor.sort}
+{ author empty$
+ { editor empty$
+ { key empty$
+ { "to sort, need author, editor, or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { editor sort.format.names }
+ if$
+ }
+ { author sort.format.names }
+ if$
+}
+
+FUNCTION {author.organization.sort}
+{ author empty$
+ { organization empty$
+ { key empty$
+ { "to sort, need author, organization, or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { "The " #4 organization chop.word sortify }
+ if$
+ }
+ { author sort.format.names }
+ if$
+}
+
+FUNCTION {editor.organization.sort}
+{ editor empty$
+ { organization empty$
+ { key empty$
+ { "to sort, need editor, organization, or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { "The " #4 organization chop.word sortify }
+ if$
+ }
+ { editor sort.format.names }
+ if$
+}
+
+FUNCTION {presort}
+{ type$ "book" =
+ type$ "inbook" =
+ or
+ 'author.editor.sort
+ { type$ "proceedings" =
+ 'editor.organization.sort
+ { type$ "manual" =
+ 'author.organization.sort
+ 'author.sort
+ if$
+ }
+ if$
+ }
+ if$
+ " "
+ *
+ year field.or.null sortify
+ *
+ " "
+ *
+ title field.or.null
+ sort.format.title
+ *
+ #1 entry.max$ substring$
+ 'sort.key$ :=
+}
+
+ITERATE {presort}
+
+SORT
+
+STRINGS { longest.label }
+
+INTEGERS { number.label longest.label.width }
+
+FUNCTION {initialize.longest.label}
+{ "" 'longest.label :=
+ #1 'number.label :=
+ #0 'longest.label.width :=
+}
+
+FUNCTION {longest.label.pass}
+{ number.label int.to.str$ 'label :=
+ number.label #1 + 'number.label :=
+ label width$ longest.label.width >
+ { label 'longest.label :=
+ label width$ 'longest.label.width :=
+ }
+ 'skip$
+ if$
+}
+
+EXECUTE {initialize.longest.label}
+
+ITERATE {longest.label.pass}
+
+FUNCTION {begin.bib}
+{ preamble$ empty$
+ 'skip$
+ { preamble$ write$ newline$ }
+ if$
+ "\begin{thebibliography}"
+ write$ newline$
+}
+
+EXECUTE {begin.bib}
+
+EXECUTE {init.state.consts}
+
+ITERATE {call.type$}
+
+FUNCTION {end.bib}
+{ newline$
+ "\end{thebibliography}" write$ newline$
+}
+
+EXECUTE {end.bib}
+%% End of customized bst file
+%%
+%% End of file `gtart.bst'.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/gtart.cls Tue Jul 01 04:00:22 2008 +0000
@@ -0,0 +1,502 @@
+%%%%%%%%%%%%%%%%%% gtart.cls %%%%%%%%%%%%%%%%%%
+%
+% Format file for articles written in LaTeX for publication in
+% Geometry & Topology and Algebraic & Geometric Topology.
+%
+% For instructions see gtartins.tex and .ps and .pdf in gt/info/macros
+%
+% Version 1.3
+%
+%% Check for fairly recent version of latex2e :
+%
+\NeedsTeXFormat{LaTeX2e}[1994/12/01]
+%
+\LoadClass[11pt]{article} % Basic style
+\usepackage{amsthm} % For GT theorem style (see below)
+%
+% Basic layout :
+%
+\newskip\stdskip % standard vertical space
+\stdskip=6.6pt plus3.3pt minus3.3pt
+%
+\setlength{\textheight}{7.5in}
+\setlength{\textwidth}{5.2in}
+\flushbottom
+\setlength{\parindent}{0pt}
+\setlength{\parskip}{\stdskip}
+\setlength{\medskipamount}{\stdskip}
+\setlength{\mathsurround}{0.8pt}
+\setlength{\labelsep}{0.75em}
+\newcommand{\stdspace}{\hskip 0.75em plus 0.15em \ignorespaces}
+\let\qua\stdspace % useful abbreviation
+%
+% Some style commands (\ppar is for principal paragraph breaks, \sh is
+% for subheadings and \rk for remarks etc -- see also theorem style
+% below ) :
+%
+\newcommand{\ppar}{\par\goodbreak\vskip 8pt plus 3pt minus 3pt}
+\newcommand{\sh}[1]{\penalty-800\ppar{\bf #1}\par\medskip\nobreak}
+\newcommand{\rk}[1]{\ppar{\bf #1}\stdspace}
+%
+%
+% Theorem style. There are two recommended styles :
+%
+% plain : for theorems, corollaries etc with heading bold
+% and left justified, optional note bracketed in roman type
+% and statement in slanted type.
+%
+% definition : (alias remark) for definitions, remarks etc with
+% heading bold and left justified, optional note unbracketed in
+% slanted type and statement in roman type.
+%
+%
+% Redefine the amsthm styles plain, definition and remark to GT style:
+%
+\newtheoremstyle{plain}{14pt plus6.3pt minus6.3pt}{7.4pt plus3pt minus3pt}%
+{\sl}{}{\bf}{}{0.75em}{\thmname{#1}\thmnumber{ #2}\thmnote{\rm\stdspace(#3)}}
+%
+\newtheoremstyle{definition}{14pt plus6.3pt minus6.3pt}{7.4pt plus3pt minus3pt}%
+{\rm}{}{\bf}{}{0.75em}{\thmname{#1}\thmnumber{ #2}\thmnote{\sl\stdspace#3}}
+%
+\newtheoremstyle{remark}{14pt plus6.3pt minus6.3pt}{7.4pt plus3pt minus3pt}%
+{\rm}{}{\bf}{}{0.75em}{\thmname{#1}\thmnumber{ #2}\thmnote{\sl\stdspace#3}}
+%
+% Default theorem style :
+\theoremstyle{plain}
+%
+% Adapt the amsthm proof environment to GT style :
+%
+\renewenvironment{proof}[1][\proofname]{\par
+ \normalfont
+ \topsep\stdskip \trivlist
+ \item[\hskip\labelsep\bf
+ #1]\ignorespaces
+}{%
+ \qed\endtrivlist\par
+}
+% Knuth's \square macro :
+%
+\def\sqr#1#2{{\vcenter{\vbox{\hrule height.#2pt
+ \hbox{\vrule width.#2pt height#1pt \kern#1pt \vrule width.#2pt}
+ \hrule height.#2pt}}}}
+%
+\def\sq{\sqr55} % A small square for end-of-proofs.
+\def\qedsymbol{$\sqr55$} % (Define other size squares by varing the
+% % the two numbers.)
+%
+% Some useful abbreviations :
+%
+\newcommand{\co}{\colon\thinspace} % Colon with correct spacing for maps.
+\newcommand{\np}{\newpage} % Forced page break (new page).
+\newcommand{\nl}{\hfil\break} % New line.
+\newcommand{\cl}{\centerline} % Centerline
+\def\gt{{\mathsurround=0pt\it $\cal G\mskip-2mu$eometry \&\
+$\cal T\!\!$opology}} % The journal title in recommended style
+\def\gtm{{\mathsurround=0pt\it $\cal G\mskip-2mu$eometry \&\
+$\cal T\!\!$opology $\cal M\mskip-1mu$onographs}} % for monographs
+\def\agt{{\mathsurround=0pt\it$\cal A\mskip-.7mu$lgebraic \&\
+$\cal G\mskip-2mu$eometric $\cal T\!\!$opology}} % AGT
+%
+% Define the various ingredients of the title page and cope with
+% all reasonable alternative syntax including amsart and article
+% style :
+%
+\def\title{\let\\\par\@ifnextchar[\doubletitle\singletitle}
+ \def\doubletitle[#1]#2{\def\thetitle{#2}\def\theshorttitle{#1}}
+ \def\singletitle#1{\def\thetitle{#1}}
+\def\shorttitle#1{\def\theshorttitle{#1}}
+%
+\def\author{\@ifnextchar[\doubleauthor\singleauthor}
+\def\singleauthor#1{\edef\previousauthors{\theauthors}
+ \ifx\theauthors\relax\def\theauthors{#1}\else
+ \def\theauthors{\previousauthors\par#1}\fi}
+\def\doubleauthor[#1]#2{\singleauthor{#2}}
+\let\authors\author\let\secondauthor\author % aliases
+\def\shortauthors#1{\def\theshortauthors{#1}}
+%
+\def\address#1{{\let\newline\par\xdef\previousaddresses{\theaddress}}
+ \ifx\theaddress\relax\def\theaddress{#1}\else
+ \def\theaddress{\previousaddresses\par\vskip 2pt\par#1}\fi}
+\let\addresses\address % alias
+\def\secondaddress#1{{\let\newline\par\xdef\previousaddresses{\theaddress}}
+ \ifx\theaddress\relax\def\theaddress{#1}\else
+ \def\theaddress{\previousaddresses\par{\rm and}\par#1}\fi}
+%
+\def\email#1{\edef\previousemails{\theemail}
+ \ifx\theemail\relax\def\theemail{#1}\else
+ \def\theemail{\previousemails\hskip 0.75em\relax#1}\fi}
+\let\emails\email\let\emailaddress\email\let\emailaddr\email % aliases
+\def\secondemail#1{\edef\previousemails{\theemail}
+ \ifx\theemail\relax\def\theemail{#1}\else
+ \def\theemail{\previousemails\hskip 0.75em{\rm and}\hskip 0.75em
+ \relax#1}\fi}
+%
+\def\url#1{\edef\previousurls{\theurl}
+ \ifx\theurl\relax\def\theurl{#1}\else
+ \def\theurl{\previousurls\hskip 0.75em\relax#1}\fi}
+\let\urls\url\let\urladdress\url\let\urladdr\url % aliases
+\def\secondurl#1{\edef\previousurls{\theurl}
+ \ifx\theurl\relax\def\theurl{#1}\else
+ \def\theurl{\previousurls\hskip 0.75em{\rm and}\hskip 0.75em
+ \relax#1}\fi}
+%
+\long\def\abstract#1\end#2#3\end#4%
+{\expandafter\ifx\csname#2\endcsname\abstract
+\long\gdef\theabstract{#1}\end{abstract}#3\end{#4}\else
+\long\gdef\theabstract{#1\end{#2}#3}\end{abstract}\fi}
+\def\endabstract{\relax}
+%
+\def\primaryclass#1{\def\theprimaryclass{#1}}
+\let\subjclass\primaryclass % alias
+\def\secondaryclass#1{\def\thesecondaryclass{#1}}
+\def\keywords#1{\def\thekeywords{#1}}
+%
+% Set \\ to \par and title page items to \relax to initialise macros :
+%
+\let\\\par\let\thetitle\relax\let\theauthors\relax
+\let\theaddress\relax\let\theemail\relax\let\theurl\relax
+\let\theabstract\relax\let\theprimaryclass\relax
+\let\thesecondaryclass\relax\let\thekeywords\relax
+\let\theshorttitle\relax\let\theshortauthors\relax
+%
+%%%% publication info and test defaults for authors:
+
+\def\volumenumber#1{\def\thevolumenumber{#1}}
+\def\volumename#1{\def\thevolumename{#1}}
+\def\volumeyear#1{\def\thevolumeyear{#1}}
+\def\pagenumbers#1#2{\def\startpage{#1}\def\finishpage{#2}}
+\def\published#1{\def\publishdate{#1}}
+
+\volumenumber{X}
+\volumename{Volume name goes here}
+\volumeyear{20XX}
+\pagenumbers{1}{XXX}
+\published{XX Xxxember 20XX}
+%
+%
+% Basic title page layout (edit this macro if you
+% wish to adjust the title page layout) :
+%
+\long\def\maketitlepage{ % start of definition of \maketitlepage
+%
+\vglue 0.2truein % top margin
+%
+% title :
+{\parskip=0pt\leftskip 0pt plus 1fil\def\\{\par\smallskip}{\Large
+\bf\thetitle}\par\medskip}
+%
+\vglue 0.15truein % space below title
+%
+% authors :
+{\parskip=0pt\leftskip 0pt plus 1fil\def\\{\par}{\sc\theauthors}
+\par\medskip}
+%
+\vglue 0.1truein % space below author(s)
+%
+% address(es) email's and URL's (with switches to detect whether the
+% optional items have been used) :
+{\parskip=0pt\small\let\newline\\
+{\leftskip 0pt plus 1fil\def\\{\par}{\sl\theaddress}\par}
+\ifx\theemail\relax\else % email address?
+\vglue 5pt \def\\{\ \ {\rm and}\ \ }
+\cl{Email:\ \ \tt\theemail}\fi
+\ifx\theurl\relax\else % URL given?
+\vglue 5pt \def\\{\ \ {\rm and}\ \ }
+\cl{URL:\ \ \tt\theurl}\fi\par}
+%
+\vglue 7pt % space below addresses
+%
+% Abstract:
+{\bf Abstract}\vglue 5pt\theabstract
+%
+\vglue 9pt % space below abstract
+%
+% AMS numbers and keywords:
+{\bf AMS Classification numbers}\quad Primary:\quad \theprimaryclass\par
+Secondary:\quad \thesecondaryclass\vglue 5pt
+{\bf Keywords:}\quad \thekeywords
+%
+\np % page break at the end of the title page
+} % end of definition of \maketitlepage
+%
+%
+%
+\long\def\makeshorttitle{ % start of definition of \makeshorttitle
+%
+% title :
+%
+{\parskip=0pt\leftskip 0pt plus 1fil\def\\{\par\smallskip}{\Large
+\bf\thetitle}\par\medskip}
+
+\vglue 0.05truein
+
+% authors :
+%
+{\parskip=0pt\leftskip 0pt plus 1fil\def\\{\par}{\sc\theauthors}
+\par\medskip}%
+
+\vglue 0.03truein
+
+% address(es) email's and URL's (with switches to detect whether the
+% optional items have been used) :
+%
+{\small\parskip=0pt
+{\leftskip 0pt plus 1fil\def\\{\par}{\sl\theaddress}\par}
+\ifx\theemail\relax\else % email address?
+\vglue 5pt \def\\{\stdspace{\rm and}\stdspace}
+\cl{Email:\stdspace\tt\theemail}\fi
+\ifx\theurl\relax\else % URL given?
+\vglue 5pt \def\\{\stdspace{\rm and}\stdspace}
+\cl{URL:\stdspace\tt\theurl}\fi\par}
+
+\vglue 10pt
+
+{\small\leftskip 25pt\rightskip 25pt{\bf Abstract}\stdspace\theabstract
+
+{\bf AMS Classification}\stdspace\theprimaryclass
+\ifx\thesecondaryclass\relax\else; \thesecondaryclass\fi\par
+{\bf Keywords}\stdspace \thekeywords\par}
+\vglue 7pt
+} % end of definition of \makeshorttitle
+%
+\let\maketitle\makeshorttitle %% alias
+%
+\long\def\makegtmontitle{ % start of definition of \makegtmontitle
+
+\count0=\startpage
+
+\gtm\nl % GT mongraphs (top left)
+{\small Volume \thevolumenumber: \thevolumename\nl
+Pages \startpage--\finishpage\nl}
+
+\vglue 0.1truein % top margin
+
+% title
+{\parskip=0pt\leftskip 0pt plus 1fil\def\\{\par\smallskip}{\Large
+\bf\thetitle}\par\medskip}
+\vglue 0.05truein
+
+% authors :
+%
+{\parskip=0pt\leftskip 0pt plus 1fil\def\\{\par}{\sc\theauthors}
+\par\medskip}%
+
+\vglue 0.03truein
+
+% abstract and classification numbers:
+
+{\small\leftskip 25pt\rightskip 25pt{\bf Abstract}\stdspace\theabstract
+
+{\bf AMS Classification}\stdspace\theprimaryclass
+\ifx\thesecondaryclass\relax\else; \thesecondaryclass\fi\par
+{\bf Keywords}\stdspace \thekeywords\par}\vglue 7pt
+
+} % end of definition of \makegtmontitle
+%
+\long\def\makeagttitle{ %%% start of definition of \makeagttitle
+\agt\hfill % Journal title (top left)
+% logo placeholder (top right)
+\hbox to 60pt{\vbox to 0pt{\vglue -14pt{\normalsize \bf [Logo here]}\vss}\hss}
+%
+\break
+{\small Volume \thevolumenumber\ (\thevolumeyear)
+\startpage--\finishpage\nl
+Published: \publishdate}
+
+\vglue .25truein
+
+% title
+{\parskip=0pt\leftskip 0pt plus
+1fil\def\\{\par\smallskip}{\Large\bf\thetitle}\par\medskip} \vglue
+0.05truein
+
+% authors :
+%
+{\parskip=0pt\leftskip 0pt plus 1fil\def\\{\par}{\sc\theauthors}
+\par\medskip}%
+
+\vglue 0.03truein
+
+% abstract and classification numbers:
+
+{\small\leftskip 25pt\rightskip 25pt{\bf Abstract}\stdspace\theabstract
+
+{\bf AMS Classification}\stdspace\theprimaryclass
+\ifx\thesecondaryclass\relax\else; \thesecondaryclass\fi\par
+{\bf Keywords}\stdspace \thekeywords\par}\vglue 7pt
+
+} %%%% end of definition of \makeagttitle
+%
+%%%% for addresses at the end of the paper:
+\def\Addresses{\bigskip
+{\small \parskip 0pt \leftskip 0pt \rightskip 0pt plus 1fil \def\\{\par}
+\sl\theaddress\par\medskip \rm Email:\stdspace\tt\theemail\par
+\ifx\theurl\relax\else\smallskip \rm URL:\stdspace\tt\theurl\par\fi}}
+
+\def\agtart{% Full mock-up of AGT article style (for authors to test with)
+% get print centerpage:
+\headsep 23pt
+\footskip 35pt
+\hoffset -4truemm
+\voffset 12.5truemm
+% fonts for headline and footline
+\font\lhead=cmsl9 scaled 1050
+\font\lnum=cmbx10
+\font\lfoot=cmsl9 scaled 1050
+% headline and footline
+\def\@oddhead{{\small\lhead\ifnum\count0=\startpage ISSN numbers
+are printed here\hfill {\lnum\number\count0}\else\ifodd\count0
+\def\\{ }\ifx\theshorttitle\relax \thetitle \else\theshorttitle\fi\hfill
+{\lnum\number\count0}\else\def\\{ and }{\lnum\number\count0}
+\hfill\ifx\theshortauthors\relax
+\theauthors\else\theshortauthors\fi\fi\fi}}\def\@evenhead{\@oddhead}
+\def\@oddfoot{\small\lfoot\ifnum\count0=\startpage Copyright
+declaration is printed here\hfill\else
+\agt, Volume \thevolumenumber\ (\thevolumeyear)\hfill\fi}
+\def\@evenfoot{\@oddfoot}
+% force \makeagttitle
+\let\maketitlepage\makeagttitle\let\maketitle\makeagttitle
+\let\makeshorttitle\makeagttitle}
+%
+\def\gtmonart{% Full mock-up of GT monograph style (for authors to test with)
+% get print centerpage:
+\headsep 23pt
+\footskip 35pt
+\hoffset -4truemm
+\voffset 12.5truemm
+% fonts for headline and footline
+\font\lhead=cmsl9 scaled 1050
+\font\lnum=cmbx10
+\font\lfoot=cmsl9 scaled 1050
+% headline and footline
+\def\@oddhead{{\small\lhead\ifnum\count0=\startpage ISSN numbers
+are printed here\hfill {\lnum\number\count0}\else\ifodd\count0
+\def\\{ }\ifx\theshorttitle\relax \thetitle \else\theshorttitle\fi\hfill
+{\lnum\number\count0}\else\def\\{ and }{\lnum\number\count0}
+\hfill\ifx\theshortauthors\relax
+\theauthors\else\theshortauthors\fi\fi\fi}}\def\@evenhead{\@oddhead}
+\def\@oddfoot{\small\lfoot\ifnum\count0=\startpage Copyright
+declaration is printed here\hfill\else
+\gtm, Volume \thevolumenumber\ (\thevolumeyear)\hfill\fi}
+\def\@evenfoot{\@oddfoot}
+% force \makegtmontitle
+\let\maketitle\makegtmontitle\let\makeshorttitle\makegtmontitle
+\let\maketitlepage\makegtmontitle}
+%
+\def\gtart{% Full mock-up of GT article style (for authors to test with)
+% get print centerpage:
+\headsep 23pt
+\footskip 35pt
+\hoffset -4truemm
+\voffset 12.5truemm
+% fonts for headline and footline
+\font\lhead=cmsl9 scaled 1050
+\font\lnum=cmbx10
+\font\lfoot=cmsl9 scaled 1050
+% headline and footline
+\def\@oddhead{{\small\lhead\ifnum\count0=\startpage ISSN numbers
+are printed here\hfill {\lnum\number\count0}\else\ifodd\count0
+\def\\{ }\ifx\theshorttitle\relax \thetitle \else\theshorttitle\fi\hfill
+{\lnum\number\count0}\else\def\\{ and }{\lnum\number\count0}
+\hfill\ifx\theshortauthors\relax
+\theauthors\else\theshortauthors\fi\fi\fi}}\def\@evenhead{\@oddhead}
+\def\@oddfoot{\small\lfoot\ifnum\count0=\startpage Copyright
+declaration is printed here\hfill\else
+\gt, Volume \thevolumenumber\ (\thevolumeyear)\hfill\fi}
+\def\@evenfoot{\@oddfoot}
+% force \maketitlepage
+\let\maketitle\maketitlepage\let\makeshorttitle\maketitlepage}
+%
+% A few definitions to adapt (or disable) various items from amsart
+% style (not already covered above) :
+%
+\def\@message#1{\immediate\write16{#1}}
+\def\thanks#1{\@message{ }
+\@message{Thanks should not appear on the title page.}
+\@message{Please give thanks as acknowledgements at the end of your
+introduction.}\@message{ }\relax}
+\def\dedicatory#1{\@message{ }
+\@message{Dedications should not appear on the title page.}
+\@message{Please give these with your acknowledgements at the end of your
+introduction.}\@message{ }\relax}
+\def\bysame{\leavevmode\hbox to3em{\hrulefill}\thinspace}
+%
+% End of macros for basic title page layout
+%
+%
+% Some hacks to get various items of style correct :
+%
+% Set footnotes in 10pt type:
+%
+\let\@footnote@\footnote
+\def\footnote#1{\@footnote@{\small #1}}
+\let\fnote\footnote % useful abbreviation for \footnote
+%
+% Set captions in 10pt type (hack of excerpt from latex.ltx) :
+%
+\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname
+ ext@#1\endcsname}{#1}{\protect\numberline{\csname
+ the#1\endcsname}{\ignorespaces #2}}\begingroup
+ \@parboxrestore
+ \small
+ \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
+ \endgroup}
+%
+% Command to suppress the colon in captions (hack from article.cls) :
+%
+\def\nocolon{%
+\long\def\@makecaption##1##2{%
+ \vskip\abovecaptionskip
+ \sbox\@tempboxa{##1##2}%
+ \ifdim \wd\@tempboxa >\hsize
+ ##1##2\par
+ \else
+ \global \@minipagefalse
+ \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}%
+ \fi
+ \vskip\belowcaptionskip}}
+%
+%
+% Set displayskips to correct values :
+%
+\let\@document@\document
+\def\document{\@document@%
+\setlength{\abovedisplayskip}{\stdskip}
+\setlength{\belowdisplayskip}{\stdskip}}
+%
+%
+% Get the biblio style correct (10pt with small gaps):
+%
+\let\@thebibliography@\thebibliography
+\def\thebibliography#1 {\@thebibliography@{999}\small\parskip0pt %
+plus2pt\relax}
+%
+%
+% Get item spacing reasonable :
+%
+\let\@itemize@\itemize
+\def\itemize{\@itemize@\parskip 0pt\relax}
+\def\@listi{\leftmargin28.5pt\parsep 0pt\topsep 0pt
+ \itemsep4pt plus3pt minus2pt}
+\let\@listI\@listi
+\@listi
+%
+\def\items{\bgroup\itemize} % for comptibility
+\def\enditems{\enditemize\egroup} % with gtmacros
+\let\itemb\item % (plain tex format)
+%
+% Get enumeration labels like plain or amstex :
+%
+\renewcommand{\labelenumi}{{\rm (\theenumi)}}
+%
+% and spacing to match \itemize:
+%
+\let\@enumerate@\enumerate
+\def\enumerate{\@enumerate@\parskip 0pt\relax}
+%
+\endinput
+%
+% History:
+% Version 1.1: 14 December 97
+% Version 1.2: (update for AGT) 18 October 00
+% Version 1.3: \gtart, \makegtmontitle and \gtmonart added 5.01.01
\ No newline at end of file
--- a/preamble.tex Tue Jul 01 01:53:15 2008 +0000
+++ b/preamble.tex Tue Jul 01 04:00:22 2008 +0000
@@ -117,6 +117,7 @@
\newcommand{\onto}{\twoheadrightarrow}
\newcommand{\iso}{\cong}
\newcommand{\actsOn}{\circlearrowright}
+\newcommand{\isoto}{\xrightarrow{\iso}}
\newcommand{\htpy}{\simeq}