--- a/pnas/pnas.tex Wed Nov 17 11:26:00 2010 -0800
+++ b/pnas/pnas.tex Wed Nov 17 11:46:39 2010 -0800
@@ -221,14 +221,27 @@
This extension is the desired derived version of a TQFT, which we call the blob complex.
(The name comes from the ``blobs" which feature prominently
in a concrete version of the homotopy colimit.)
-
-\nn{In many places we omit details; they can be found in MW.
-(Blanket statement in order to avoid too many citations to MW.)}
+We then review some basic properties of the blob complex, and finish by showing how it
+yields a higher categorical and higher dimensional generalization of Deligne's
+conjecture on Hochschild cochains and the little 2-disks operad.
-\nn{perhaps say something explicit about the relationship of this paper to big blob paper.
-like: in this paper we try to give a clear view of the big picture without getting bogged down in details}
+\nn{maybe this is not necessary?}
+In an attempt to forestall any confusion that might arise from different definitions of
+``$n$-category" and ``TQFT", we note that our $n$-categories are both more and less general
+than the ``fully dualizable" ones which play a prominent role in \cite{0905.0465}.
+More general in that we make no duality assumptions in the top dimension $n+1$.
+Less general in that we impose stronger duality requirements in dimensions 0 through $n$.
+Thus our $n$-categories correspond to $(n{+}\epsilon)$-dimensional unoriented or oriented TQFTs, while
+Lurie's (fully dualizable) $n$-categories correspond to $(n{+}1)$-dimensional framed TQFTs.
-\nn{diff w/ lurie}
+Details missing from this paper can usually be found in \cite{1009.5025}.
+
+%\nn{In many places we omit details; they can be found in MW.
+%(Blanket statement in order to avoid too many citations to MW.)}
+%
+%\nn{perhaps say something explicit about the relationship of this paper to big blob paper.
+%like: in this paper we try to give a clear view of the big picture without getting bogged down in details}
+
\section{Definitions}
\subsection{$n$-categories} \mbox{}