--- a/text/definitions.tex Sun Nov 01 20:29:33 2009 +0000
+++ b/text/definitions.tex Sun Nov 01 20:29:41 2009 +0000
@@ -27,8 +27,6 @@
is a collection of functors $\cC_k : \cM_k \to \Set$ for $0 \leq k \leq n$
together with some additional data and satisfying some additional conditions, all specified below.
-\nn{refer somewhere to my TQFT notes \cite{kw:tqft}}
-
Before finishing the definition of fields, we give two motivating examples
(actually, families of examples) of systems of fields.
@@ -390,7 +388,7 @@
\end{itemize}
(See Figure \ref{blob1diagram}.)
\begin{figure}[!ht]\begin{equation*}
-\mathfig{.9}{tempkw/blob1diagram}
+\mathfig{.9}{definition/single-blob}
\end{equation*}\caption{A 1-blob diagram.}\label{blob1diagram}\end{figure}
In order to get the linear structure correct, we (officially) define
\[
@@ -423,11 +421,11 @@
\item A pair of closed balls (blobs) $B_0, B_1 \sub X$ with disjoint interiors.
\item A field $r \in \cC(X \setmin (B_0 \cup B_1); c_0, c_1)$
(where $c_i \in \cC(\bd B_i)$).
-\item Local relation fields $u_i \in U(B_i; c_i)$, $i=1,2$.
+\item Local relation fields $u_i \in U(B_i; c_i)$, $i=1,2$. \nn{We're inconsistent with the indexes -- are they 0,1 or 1,2? I'd prefer 1,2.}
\end{itemize}
(See Figure \ref{blob2ddiagram}.)
\begin{figure}[!ht]\begin{equation*}
-\mathfig{.9}{tempkw/blob2ddiagram}
+\mathfig{.9}{definition/disjoint-blobs}
\end{equation*}\caption{A disjoint 2-blob diagram.}\label{blob2ddiagram}\end{figure}
We also identify $(B_0, B_1, u_0, u_1, r)$ with $-(B_1, B_0, u_1, u_0, r)$;
reversing the order of the blobs changes the sign.
@@ -447,7 +445,7 @@
\end{itemize}
(See Figure \ref{blob2ndiagram}.)
\begin{figure}[!ht]\begin{equation*}
-\mathfig{.9}{tempkw/blob2ndiagram}
+\mathfig{.9}{definition/nested-blobs}
\end{equation*}\caption{A nested 2-blob diagram.}\label{blob2ndiagram}\end{figure}
Let $r = r_1 \bullet r'$, where $r_1 \in \cC(B_1 \setmin B_0; c_0, c_1)$
(for some $c_1 \in \cC(B_1)$) and