%auto-ignore %!TEX root = article.tex %this ensures the arxiv doesn't try to start TeXing here. \newcommand{\forGTART}[1]{#1} \newcommand{\forQT}[1]{} \newcommand{\forOUP}[1]{} \usepackage{ifthen} %\ifthenelse{\equal{\ClassName}{QT}} % {\renewcommand{\forQT}[1]{#1}} % {\renewcommand{\forGTART}[1]{#1}} \usepackage{amsmath,amssymb,amsfonts} \usepackage{ifpdf} \usepackage{enumerate} \usepackage{ulem} \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 % ---------------------------------------------------------------- % 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{\baselinetrick}[1]{\hspace{-3pt}\begin{array}{c}% \raisebox{-2.5pt}{#1}% \end{array}\hspace{-3pt}} \newcommand{\mathfig}[2]{\ensuremath{\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{\pathtotrunk diagrams/tikz/#1.tex}} \newcommand{\arxiv}[1]{Preprint \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})} \def\RCS$#1: #2 ${\expandafter\def\csname RCS#1\endcsname{#2}} \RCS$Revision$ \RCS$Date$ \newcommand{\versioninfo}{Version \RCSRevision; Last commit \RCSDate} % THEOREMS ------------------------------------------------------- \theoremstyle{plain} \newtheorem{prop}{Proposition}[section] \newtheorem{conj}[prop]{Conjecture} \newtheorem{thm}[prop]{Theorem} \newtheorem{ex}[prop]{Example} \newtheorem*{thm*}{Theorem} \newtheorem{recipe}[prop]{Recipe} \newtheorem{project}[prop]{Project} \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} \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{$\mathsurround=0pt#1{#2}$}} % mathematica -------------------------------------------------- \newcommand{\code}[1]{{\tt #1}} \newcommand{\package}[1]{\code{#1`}} \newcommand{\MMA}{Mathematica{}} \newenvironment{mma}{}{} \newcounter{lineNumber} \newcommand{\inN}{\stepcounter{lineNumber}\arabic{lineNumber}} \newcommand{\outN}{\arabic{lineNumber}} \newenvironment{inm}{% \vskip 0pt \par\noindent% {\footnotesize\color{blue}In[\inN]$:=$}\tt% }{} \newenvironment{outm}{% \vskip -6pt \par\noindent\parindent=12pt% {\footnotesize\color{blue}Out[\outN]$=$}\tt% }{} \newenvironment{printm}% {\begin{quotation}\noindent}% {\end{quotation}}% % 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{\cA}{\mathcal{A}} \newcommand{\cB}{\mathcal{B}} \newcommand{\cC}{\mathcal{C}} \newcommand{\cD}{\mathcal{D}} \newcommand{\cE}{\mathcal{E}} \newcommand{\cF}{\mathcal{F}} \newcommand{\cG}{\mathcal{G}} \newcommand{\cH}{\mathcal{H}} \newcommand{\cI}{\mathcal{I}} \newcommand{\cJ}{\mathcal{J}} \newcommand{\cK}{\mathcal{K}} \newcommand{\cL}{\mathcal{L}} \newcommand{\cM}{\mathcal{M}} \newcommand{\cN}{\mathcal{N}} \newcommand{\cO}{\mathcal{O}} \newcommand{\cP}{\mathcal{P}} \newcommand{\cQ}{\mathcal{Q}} \newcommand{\cR}{\mathcal{R}} \newcommand{\cS}{\mathcal{S}} \newcommand{\cT}{\mathcal{T}} \newcommand{\cU}{\mathcal{U}} \newcommand{\cV}{\mathcal{V}} \newcommand{\cW}{\mathcal{W}} \newcommand{\cX}{\mathcal{X}} \newcommand{\cY}{\mathcal{Y}} \newcommand{\cZ}{\mathcal{Z}} \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{\into}{\hookrightarrow} \newcommand{\onto}{\mapsto} \newcommand{\iso}{\cong} \newcommand{\actsOn}{\circlearrowright} \newcommand{\htpy}{\simeq} \newcommand{\abs}[1]{\left|#1\right|} \newcommand{\floor}[1]{\left\lfloor#1\right\rfloor} \newcommand{\ceil}[1]{\left\lceil#1\right\rceil} \newcommand{\restrict}[2]{#1{}_{\mid #2}{}} \newcommand{\set}[1]{\left\{#1\right\}} \newcommand{\setc}[2]{\left\{#1 \;\left| \; 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