
diff -r 4a988e00468a -r a60c035e53bd text/tqftreview.tex
--- a/text/tqftreview.tex	Wed Aug 25 22:58:41 2010 -0700
+++ b/text/tqftreview.tex	Thu Aug 26 13:20:13 2010 -0700
@@ -115,7 +115,60 @@
 Let $\bd X = (Y \du Y) \cup W$, where the two copies of $Y$ 
 are disjoint from each other and $\bd(Y\du Y) = \bd W$.
 Let $X\sgl$ denote $X$ glued to itself along the two copies of $Y$
-(Figure \ref{fig:???}).
+(Figure \ref{fig:gluing-with-corners}).
+\begin{figure}[t]
+\begin{center}
+\begin{tikzpicture}
+
+\node(A) at (-4,0) {
+\begin{tikzpicture}[scale=.8, fill=blue!15!white]
+\filldraw[line width=1.5pt] (-.4,1) .. controls +(-1,-.1) and +(-1,0) .. (0,-1)
+		.. controls +(1,0) and +(1,-.1) .. (.4,1) -- (.4,3)
+		.. controls +(3,-.4) and +(3,0) .. (0,-3)
+		.. controls +(-3,0) and +(-3,-.1) .. (-.4,3) -- cycle;
+\node at (0,-2) {$X$};
+\node (W) at (-2.7,-2) {$W$};
+\node (Y1) at (-1.2,3.5) {$Y$};
+\node (Y2) at (1.4,3.5) {$Y$};
+\node[outer sep=2.3] (y1e) at (-.4,2) {};
+\node[outer sep=2.3] (y2e) at (.4,2) {};
+\node (we1) at (-2.2,-1.1) {};
+\node (we2) at (-.6,-.7) {};
+\draw[->] (Y1) -- (y1e);
+\draw[->] (Y2) -- (y2e);
+\draw[->] (W) .. controls +(0,.5) and +(-.5,-.2) .. (we1);
+\draw[->] (W) .. controls +(.5,0) and +(-.2,-.5) .. (we2);
+\end{tikzpicture}
+};
+
+\node(B) at (4,0) {
+\begin{tikzpicture}[scale=.8, fill=blue!15!white]
+\fill (0,1) .. controls +(-1,0) and +(-1,0) .. (0,-1)
+		.. controls +(1,0) and +(1,0) .. (0,1) -- (0,3)
+		.. controls +(3,0) and +(3,0) .. (0,-3)
+		.. controls +(-3,0) and +(-3,0) .. (0,3) -- cycle;
+\draw[line width=1.5pt] (0,1) .. controls +(-1,0) and +(-1,0) .. (0,-1)
+		.. controls +(1,0) and +(1,0) .. (0,1);
+\draw[line width=1.5pt] (0,3) .. controls +(3,0) and +(3,0) .. (0,-3)
+		.. controls +(-3,0) and +(-3,0) .. (0,3);
+\draw[line width=.5pt, black!65!white] (0,1) -- (0,3);
+\node at (0,-2) {$X\sgl$};
+\node (W) at (2.7,-2) {$W\sgl$};
+\node (we1) at (2.2,-1.1) {};
+\node (we2) at (.6,-.7) {};
+\draw[->] (W) .. controls +(0,.5) and +(.5,-.2) .. (we1);
+\draw[->] (W) .. controls +(-.5,0) and +(.2,-.5) .. (we2);
+\end{tikzpicture}
+};
+
+
+\draw[->, red!50!green, line width=2pt] (A) -- node[above, black] {glue} (B);
+
+\end{tikzpicture}
+\end{center}
+\caption{Gluing with corners}
+\label{fig:gluing-with-corners}
+\end{figure}
 Note that $\bd X\sgl = W\sgl$, where $W\sgl$ denotes $W$ glued to itself
 (without corners) along two copies of $\bd Y$.
 Let $c\sgl \in \cC_{k-1}(W\sgl)$ be a be a splittable field on $W\sgl$ and let




