diff -r 1b3ebb7793c9 -r d13df7f3b2de text/intro.tex --- a/text/intro.tex Tue Mar 02 21:52:01 2010 +0000 +++ b/text/intro.tex Wed Mar 03 20:17:52 2010 +0000 @@ -5,7 +5,7 @@ We construct the ``blob complex'' $\bc_*(M; \cC)$ associated to an $n$-manifold $M$ and a ``linear $n$-category with strong duality'' $\cC$. This blob complex provides a simultaneous generalisation of several well-understood constructions: \begin{itemize} \item The vector space $H_0(\bc_*(M; \cC))$ is isomorphic to the usual topological quantum field theory invariant of $M$ associated to $\cC$. (See \S \ref{sec:fields} \nn{more specific}.) -\item When $n=1$, $\cC$ is just an associative algebroid, and $\bc_*(S^1; \cC)$ is quasi-isomorphic to the Hochschild complex $\HC_*(\cC)$. (See \S \ref{sec:hochschild}.) +\item When $n=1$, $\cC$ is just a 1-category (e.g.\ an associative algebra), and $\bc_*(S^1; \cC)$ is quasi-isomorphic to the Hochschild complex $\HC_*(\cC)$. (See \S \ref{sec:hochschild}.) \item When $\cC$ is the polynomial algebra $k[t]$, thought of as an n-category (see \S \ref{sec:comm_alg}), we have that $\bc_*(M; k[t])$ is homotopy equivalent to $C_*(\Sigma^\infty(M), k)$, the singular chains on the configurations space of unlabeled points in $M$.