Binary file diagrams/pdf/tempkw/dfig1.pdf has changed
Binary file diagrams/pdf/tempkw/dfig2.pdf has changed
Binary file diagrams/pdf/tempkw/dfig3.pdf has changed
--- a/text/deligne.tex Sat May 29 20:13:23 2010 -0700
+++ b/text/deligne.tex Sat May 29 23:08:36 2010 -0700
@@ -37,7 +37,7 @@
\to \hom(\bc^C_*(I), \bc^C_*(I)) .
\]
See Figure \ref{delfig1}.
-\begin{figure}[!ht]
+\begin{figure}[t]
$$\mathfig{.9}{deligne/intervals}$$
\caption{A fat graph}\label{delfig1}\end{figure}
We emphasize that in $\hom(\bc^C_*(I), \bc^C_*(I))$ we are thinking of $\bc^C_*(I)$ as a module
@@ -65,9 +65,9 @@
involved were 1-dimensional.
Thus we can define an $n$-dimensional fat graph to be a sequence of general surgeries
on an $n$-manifold (Figure \ref{delfig2}).
-\begin{figure}[!ht]
+\begin{figure}[t]
$$\mathfig{.9}{deligne/manifolds}$$
-\caption{An $n$-dimensional fat graph}\label{delfig2}
+\caption{An $n$-dimensional fat graph}\label{delfig2}
\end{figure}
More specifically, an $n$-dimensional fat graph ($n$-FG for short) consists of:
@@ -88,7 +88,11 @@
\end{itemize}
We can think of the above data as encoding the union of the mapping cylinders $C(f_0),\ldots,C(f_k)$,
with $C(f_i)$ glued to $C(f_{i+1})$ along $R_{i+1}$
-(see Figure xxxx).
+(see Figure \ref{xdfig2}).
+\begin{figure}[t]
+$$\mathfig{.9}{tempkw/dfig2}$$
+\caption{$n$-dimensional fat graph from mapping cylinders}\label{xdfig2}
+\end{figure}
The $n$-manifolds are the ``$n$-dimensional graph" and the $I$ direction of the mapping cylinders is the ``fat" part.
We regard two such fat graphs as the same if there is a homeomorphism between them which is the
identity on the boundary and which preserves the 1-dimensional fibers coming from the mapping
@@ -102,7 +106,11 @@
\end{eqnarray*}
leaving the $M_i$ and $N_i$ fixed.
(Keep in mind the case $R'_i = R_i$.)
-(See Figure xxxx.)
+(See Figure \ref{xdfig3}.)
+\begin{figure}[t]
+$$\mathfig{.9}{tempkw/dfig3}$$
+\caption{Conjugating by a homeomorphism}\label{xdfig3}
+\end{figure}
\item If $M_i = M'_i \du M''_i$ and $N_i = N'_i \du N''_i$ (and there is a
compatible disjoint union of $\bd M = \bd N$), we can replace
\begin{eqnarray*}
@@ -112,7 +120,11 @@
(\ldots, R_{i-1}, R_i\cup M''_i, R_i\cup N'_i, R_{i+1}, \ldots) \\
(\ldots, f_{i-1}, f_i, \ldots) &\to& (\ldots, f_{i-1}, \rm{id}, f_i, \ldots) .
\end{eqnarray*}
-(See Figure xxxx.)
+(See Figure \ref{xdfig1}.)
+\begin{figure}[t]
+$$\mathfig{.9}{tempkw/dfig1}$$
+\caption{Changing the order of a surgery}\label{xdfig1}
+\end{figure}
\end{itemize}
Note that the second equivalence increases the number of holes (or arity) by 1.