--- a/text/intro.tex Tue Sep 21 07:37:41 2010 -0700
+++ b/text/intro.tex Tue Sep 21 14:44:17 2010 -0700
@@ -8,7 +8,7 @@
\begin{itemize}
\item The 0-th homology $H_0(\bc_*(M; \cC))$ is isomorphic to the usual
topological quantum field theory invariant of $M$ associated to $\cC$.
-(See Theorem \ref{thm:skein-modules} later in the introduction and \S \ref{sec:constructing-a-tqft}.)
+(See Proposition \ref{thm:skein-modules} later in the introduction and \S \ref{sec:constructing-a-tqft}.)
\item When $n=1$ and $\cC$ is just a 1-category (e.g.\ an associative algebra),
the blob complex $\bc_*(S^1; \cC)$ is quasi-isomorphic to the Hochschild complex $\HC_*(\cC)$.
(See Theorem \ref{thm:hochschild} and \S \ref{sec:hochschild}.)
@@ -124,7 +124,7 @@
} (FU.100);
\draw[->] (C) -- node[above left=3pt] {restrict to \\ standard balls} (tC);
\draw[->] (FU.80) -- node[right] {restrict \\ to balls} (C.-80);
-\draw[->] (BC) -- node[right] {$H_0$ \\ c.f. Theorem \ref{thm:skein-modules}} (A);
+\draw[->] (BC) -- node[right] {$H_0$ \\ c.f. Proposition \ref{thm:skein-modules}} (A);
\draw[->] (FU) -- node[left] {blob complex \\ for balls} (Cs);
\draw[<->] (BC) -- node[right] {$\iso$ by \\ Corollary \ref{cor:new-old}} (BCs);
@@ -286,7 +286,7 @@
The blob complex is a simultaneous generalization of the TQFT skein module construction and of Hochschild homology.
-\newtheorem*{thm:skein-modules}{Theorem \ref{thm:skein-modules}}
+\newtheorem*{thm:skein-modules}{Proposition \ref{thm:skein-modules}}
\begin{thm:skein-modules}[Skein modules]
The $0$-th blob homology of $X$ is the usual
@@ -308,7 +308,7 @@
\end{equation*}
\end{thm:hochschild}
-Theorem \ref{thm:skein-modules} is immediate from the definition, and
+Proposition \ref{thm:skein-modules} is immediate from the definition, and
Theorem \ref{thm:hochschild} is established in \S \ref{sec:hochschild}.
We also note \S \ref{sec:comm_alg} which describes the blob complex when $\cC$ is a one of
certain commutative algebras thought of as $n$-categories.