
diff -r a7b53f6a339d -r 0daa4983d229 text/ncat.tex
--- a/text/ncat.tex	Wed Jun 23 18:37:25 2010 -0700
+++ b/text/ncat.tex	Wed Jun 23 22:43:26 2010 -0700
@@ -1967,7 +1967,14 @@
 (Here we are overloading notation and letting $D$ denote both a decorated and an undecorated
 manifold.)
 We have $\bd X_i = Y_i \cup \ol{Y}_i \cup (D\times I)$
-(see Figure xxxx).
+(see Figure \ref{jun23a}).
+\begin{figure}[t]
+\begin{equation*}
+\mathfig{.6}{tempkw/jun23a}
+\end{equation*}
+\caption{$Y\times I$ sliced open}
+\label{jun23a}
+\end{figure}
 Given $a_i\in \cS(Y_i)$, $b_i\in \cS(\ol{Y}_i)$ and $v\in\cS(D\times I)$
 which agree on their boundaries, we can evaluate
 \[
@@ -2008,7 +2015,14 @@
 		\cS(A\cup B\cup \ol{B})  \stackrel{\id\ot\psi}{\longrightarrow}
 			\cS(A\cup(D\times I)) \stackrel{\cong}{\longrightarrow} \cS(A) .
 \]
-(See Figure xxxx.)
+(See Figure \ref{jun23b}.)
+\begin{figure}[t]
+\begin{equation*}
+\mathfig{.5}{tempkw/jun23b}
+\end{equation*}
+\caption{Moving $B$ from top to bottom}
+\label{jun23b}
+\end{figure}
 Let $D' = B\cap C$.
 Using the inner products there is an adjoint map
 \[
@@ -2022,6 +2036,15 @@
 			\cS(C\cup \ol{B}\cup B)   \stackrel{f'\ot\id}{\longrightarrow}
 				\cS(A\cup B) .
 \]
+(See Figure \ref{jun23c}.)
+\begin{figure}[t]
+\begin{equation*}
+\mathfig{.5}{tempkw/jun23c}
+\end{equation*}
+\caption{Moving $B$ from bottom to top}
+\label{jun23c}
+\end{figure}
+Let $D' = B\cap C$.
 It is not hard too show that the above two maps are mutually inverse.
 
 \begin{lem}
@@ -2049,7 +2072,14 @@
 
 The second movie move replaces to successive pushes in the same direction,
 across $B_1$ and $B_2$, say, with a single push across $B_1\cup B_2$.
-(See Figure xxxx.)
+(See Figure \ref{jun23d}.)
+\begin{figure}[t]
+\begin{equation*}
+\mathfig{.9}{tempkw/jun23d}
+\end{equation*}
+\caption{A movie move}
+\label{jun23d}
+\end{figure}
 Invariance under this movie move follows from the compatibility of the inner
 product for $B_1\cup B_2$ with the inner products for $B_1$ and $B_2$.
 




