%auto-ignore %this ensures the arxiv doesn't try to start TeXing here. \usepackage{amsmath,amssymb,amsfonts} \usepackage{ifpdf} \usepackage[usenames]{color} \usepackage{enumerate} \usepackage{leftidx} \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 % ---------------------------------------------------------------- \def\RCS$#1: #2 ${\expandafter\def\csname RCS#1\endcsname{#2}} \RCS$Revision$ \RCS$Date$ \newcommand{\versioninfo}{Version \RCSRevision; Last commit \RCSDate} % 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}} \newcommand{\inputtikz}[1]{\input{diagrams/tikz/#1.tex}} \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{\euclid}[1]{\href{http://projecteuclid.org/getRecord?id=#1}{{\tt #1}}} \newcommand{\mathscinet}[1]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{\tt #1}} \newcommand{\googlebooks}[1]{(preview at \href{http://books.google.com/books?id=#1}{google books})} \newcommand{\numdam}[1]{} % THEOREMS ------------------------------------------------------- \theoremstyle{plain} \newtheorem*{fact}{Fact} \newtheorem{prop}{Proposition}[section] \newtheorem{conj}[prop]{Conjecture} \newtheorem{thm}[prop]{Theorem} \newtheorem{lem}[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} \newtheorem*{kuperberg}{The Kuperberg Program} \newtheorem*{mainthm}{The Main Theorem} \newtheorem*{convention}{Convention} \newenvironment{rem}{\noindent\textsl{Remark.}}{} % perhaps looks better than rem above? \numberwithin{equation}{section} %\numberwithin{figure}{section} \newcommand{\noqed}{\renewcommand{\qedsymbol}{}} % Marginal notes in draft mode ----------------------------------- \newcommand{\scott}[1]{\stepcounter{comment}{{\color{green} $\star^{(\arabic{comment})}$}}\marginpar{\color{green} $\star^{(\arabic{comment})}$ \usefont{T1}{scott}{m}{n} #1 --S}} % draft mode \newcommand{\eep}[1]{\stepcounter{comment}{\color{blue} $\star^{(\arabic{comment})}$}\marginpar{\color{blue} $\star^{(\arabic{comment})}$ #1 --E}} % draft mode \newcommand{\noah}[1]{\stepcounter{comment}{\color{red} $\star^{(\arabic{comment})}$}\marginpar{\color{red} $\star^{(\arabic{comment})}$ #1 --N}} % 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{\abs}[1]{\left|#1\right|} \newcommand{\restrict}[2]{#1{}_{\mid #2}{}} \newcommand{\set}[1]{\left\{#1\right\}} \newcommand{\setc}[2]{\left\{#1 \;\left| \; #2 \right. \right\}} \newcommand{\quotient}[2]{\frac{#1}{#2}} \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{\J}[2]{\mathcal{J}_{#1,#2}} \newcommand{\card}[1]{\sharp{#1}} \newcommand{\bdy}{\partial} \newcommand{\compose}{\circ} \newcommand{\eset}{\emptyset} \newcommand{\disj}{\sqcup} \newcommand{\cC}{\mathcal{C}} \newcommand{\psmallmatrix}[1]{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)} \newcommand{\floor}[1]{\left\lfloor#1\right\rfloor} \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{\C}{\mathcal{C}} \newcommand{\altTensor}{\widehat{\Tensor}} \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]{\operatorname{\mathbf{Mat}}\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{\im}{\operatorname{im}} \newcommand{\asbimod}[2]{\operatorname{Mod}'\left(#1 \subset #2\right)} \newcommand{\sbimod}[2]{\operatorname{Mod}\left(#1 \subset #2\right)} \newcommand{\abimod}[2]{#1-\operatorname{Mod}'-#2} \newcommand{\bimod}[2]{#1-\operatorname{Mod}-#2} \newcommand{\bimodule}[3]{\leftidx{_#1}{#2}{_#3}} \newcommand{\pa}{\mathcal{PA}(S)} \newcommand{\TL}{\mathcal{TL}} \newcommand{\JW}[1]{f^{(#1)}} \newcommand{\tr}[1]{\text{tr}(#1)} \newcommand{\dn}[1]{{\mathcal D}{\mathit (#1)}} \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]} \newcommand{\tensorover}[1]{\otimes_{#1}} \newcommand{\tensorhat}{\widehat{\Tensor}} \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}} % ----------------------------------------------------------------