\documentclass[12pt,reqno]{amsart}
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\usepackage{
  fullpage,graphicx,dbnsymb,amsmath,amssymb,floatflt,picins,
  multicol,mathtools,stmaryrd,xcolor,tensor,needspace
}
\usepackage{hyperref}

% Following http://tex.stackexchange.com/a/847/22475:
\usepackage{hyperref}\hypersetup{colorlinks,
   linkcolor={green!50!black},
   citecolor={green!50!black},
   urlcolor=blue
}

\usepackage{xr}
\externaldocument[1-]{WKO1}

\usepackage[all]{xy}

\if\draft y
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\fi

\input macros.tex
\input defs.tex

\setlength{\marginparwidth}{0.8in}

\begin{document}
\newdimen\captionwidth\captionwidth=\hsize
\setcounter{secnumdepth}{4}

\title{Extra Figures}

\author{Dror~Bar-Natan}
\address{
  Department of Mathematics\\
  University of Toronto\\
  Toronto Ontario M5S 2E4\\
  Canada
}
\email{drorbn@math.toronto.edu}
\urladdr{http://www.math.toronto.edu/~drorbn}

\author{Zsuzsanna Dancso}
\address{
  Mathematical Sciences Institute\\
  Australian National University\\
  John Dedman Bldg 26\\
  Acton ACT 2601, Australia
}
\email{zsuzsanna.dancso@anu.edu.au}
\urladdr{http://www.math.toronto.edu/zsuzsi}

\date{first edition August 7, 2023, this edition \today.}


\maketitle

\noindent(0)
\[
  \def\goesto{{$\overset{\pi}{\longmapsto} -[[x_1,x_2],[x_2,x_3]]$}}
  \input{figs/ArrowsToLie.pstex_t}
\]

\noindent(1-1) figs/wTFgensWen@:
\[
  \wTF=\CA\!\left\langle\left.\left.
  \raisebox{-6mm}{\input{figs/wTFgensWen@.pstex_t}}
  \right|
  \parbox{1.9in}{\centering \Rs, R2, R3, R4, OC, CP, FR, $W^2$, CW, TV}
  \right|
  \parbox{0.9in}{\centering $S_e, A_e, u_e, d_e$}
  \right\rangle.
\]

\noindent(1-2)
\begin{center} \input figs/FlipRels2@.pstex_t \end{center}

\noindent(1-3)
\parpic[r]{$\input{figs/CapWen@.pstex_t}$}
A cap can slide through a wen, hence a capped wen disappears, as shown
on the right, to be denoted \glost{CW}.

\noindent(1-4) figs/TVRel:
\begin{center} \input figs/TVRel.pstex_t \end{center}

\noindent(1-5)
\begin{center} \input{figs/Wen2@.pstex_t} \end{center}

\noindent(1-6) figs/SkelGenWen:
\[
  \calS = \CA\!\left\langle\left.
  \raisebox{-2mm}{\input{figs/SkelGenWen.pstex_t}}
  \right|
    \text{$W^2$, CW, TV}
  \right\rangle.
\]

\noindent(1-7)
\begin{center} \input figs/BlueR4.pstex_t \end{center}

\noindent(1-8)
\begin{center} \input figs/BlueR2.pstex_t \end{center}

\noindent(1-9) figs/AdjointV:
\begin{center} \input figs/AdjointV.pstex_t \end{center}

\noindent(1-10) figs/wTFprojgens@ (appears in two places!):

\[ \calA^{(s)w}=\CA\!\left.\left.\left\langle
  \raisebox{-6mm}{\input{figs/wTFprojgens@.pstex_t}}
  \right|
  \parbox{1.2in}{\centering relations as in Section~\ref{subsubsec:wTFGradRels}}
  \right|
  \parbox{1.2in}{\centering operations as in Section~\ref{subsubsec:wTFGradOps}}
  \right\rangle.
\]

\[ \calA^{(s)w}=\CA\!\left.\left.\left\langle
  \raisebox{-6mm}{\input{figs/wTFprojgens@.pstex_t}}
  \right|
  \parbox{1.4in}{\centering $\aft$, TC, VI, CP, $W^2$, TW, CW, FR, (RI for $\calA^{sw}$)}
  \right|
  \parbox{1.0in}{\centering $S_e, A_e, u_e, d_e$}
  \right\rangle.
\]

\noindent(1-11) figs/VI@:
\begin{center} \input figs/VI@.pstex_t \end{center}

\noindent(2-1) figs/ZofWen1:
\begin{center} \input figs/ZofWen1.pstex_t \end{center}

\needspace{20mm}
\noindent(2-2) figs/ZofWen2:
\begin{center} {\def\ol{\overline}\input{figs/ZofWen2.pstex_t}} \end{center}

\noindent(2-3) figs/ZofWen3: (Cancelled)
\begin{center} \input figs/ZofWen3.pstex_t \end{center}

\noindent(2-4) figs/ZofWen4: (Postponed)
%\begin{center} \input figs/ZofWen4.pstex_t \end{center}

\noindent(2-5) figs/ColouredCrossings:
\begin{center} \input{figs/ColouredCrossings.pstex_t} \end{center}

\noindent(3-1) figs/FRCalc:
{
  \def\ol{\overline}
  \def\Rea{$R=e^a$}
  \def\RbarR{$\ol{R}\!=\!e^{-a}\!=\!R^{-1}$}
  \def\BoB{{\raisebox{-1.75mm}{\input{figs/BlueOverBlackMinus.pstex_t}}}}
  \def\ZBoB{$Z\left(\BoB\right)^{21}$}
  \begin{center} \input{figs/FRCalc.pstex_t} \end{center}
  \begin{center} The proof of $(R^{-1})^{21} = Z\left(\BoB\right)$ \end{center}
}

\noindent(3-2) figs/TVUnitarity:
{
  \def\SSV{$S_1S_2(V^{-1})$}
  \def\OV{$\overline{V}$}
  \def\OW{$\overline{W}$}
  \begin{center} \input{figs/TVUnitarity.pstex_t} \end{center}
}

\noindent(3-3) figs/SkelGen:
\[
  \calS^0 = \CA\!\left\langle\raisebox{-2mm}{\input{figs/SkelGen.pstex_t}}\right\rangle
\]


\end{document}
\endinput

