diff -r 4d2dad357a49 -r c9f41c18a96f text/intro.tex --- 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.