# HG changeset patch
# User Scott Morrison <scott@tqft.net>
# Date 1291144044 28800
# Node ID c21da249a015fd909aea18df44a68c78617f0905
# Parent  a064476a32652233027e5343a10fe613fc0ea80a
minor changes to abstract, and blob diagrams

diff -r a064476a3265 -r c21da249a015 pnas/pnas.tex
--- a/pnas/pnas.tex	Mon Nov 29 10:01:34 2010 -0700
+++ b/pnas/pnas.tex	Tue Nov 30 11:07:24 2010 -0800
@@ -136,12 +136,10 @@
 \begin{article}
 
 \begin{abstract}
-\nn{needs revision}
-We explain the need for new axioms for topological quantum field theories that include ideas from derived 
-categories and homotopy theory. We summarize our axioms for higher categories, and describe the ``blob complex". 
+We summarize our axioms for higher categories, and describe the ``blob complex". 
 Fixing an $n$-category $\cC$, the blob complex associates a chain complex $\bc_*(W;\cC)$ to any $n$-manifold $W$. 
-The $0$-th homology of this chain complex recovers the usual TQFT invariants of $W$. 
-The higher homology groups should be viewed as generalizations of Hochschild homology. 
+The $0$-th homology of this chain complex recovers the usual topological quantum field theory invariants of $W$. 
+The higher homology groups should be viewed as generalizations of Hochschild homology (indeed, when $W=S^1$ they coincide). 
 The blob complex has a very natural definition in terms of homotopy colimits along decompositions of the manifold $W$. 
 We outline the important properties of the blob complex, and sketch the proof of a generalization of 
 Deligne's conjecture on Hochschild cohomology and the little discs operad to higher dimensions.
@@ -654,7 +652,7 @@
 such that
 \begin{itemize}
 	\item there is a permissible decomposition of $W$, compatible with the $k$ blobs, such that
-	$s$ is the product of linear combinations of fields $s_i$ on the initial pieces $X_i$ of the decomposition
+	$s$ is the result of gluing together linear combinations of fields $s_i$ on the initial pieces $X_i$ of the decomposition
 	(for fixed restrictions to the boundaries of the pieces),
 	\item the $s_i$'s corresponding to innermost blobs evaluate to zero in $\cC$, and
 	\item the $s_i$'s corresponding to the other pieces are single fields (linear combinations with only one term).