Binary file RefereeReport.pdf has changed
--- a/text/blobdef.tex Thu Aug 11 12:50:50 2011 -0700
+++ b/text/blobdef.tex Thu Aug 11 13:23:33 2011 -0700
@@ -43,7 +43,7 @@
``the space of all local relations that can be imposed on $\bc_0(X)$".
Thus we say a $1$-blob diagram consists of:
\begin{itemize}
-\item An closed ball in $X$ (``blob") $B \sub X$.
+\item A closed ball in $X$ (``blob") $B \sub X$.
\item A boundary condition $c \in \cF(\bdy B) = \cF(\bd(X \setmin B))$.
\item A field $r \in \cF(X \setmin B; c)$.
\item A local relation field $u \in U(B; c)$.
--- a/text/hochschild.tex Thu Aug 11 12:50:50 2011 -0700
+++ b/text/hochschild.tex Thu Aug 11 13:23:33 2011 -0700
@@ -12,7 +12,7 @@
Hochschild complex of the 1-category $\cC$.
(Recall from \S \ref{sec:example:traditional-n-categories(fields)} that a
$1$-category gives rise to a $1$-dimensional system of fields; as usual,
-talking about the blob complex with coefficients in a $n$-category means
+talking about the blob complex with coefficients in an $n$-category means
first passing to the corresponding $n$ dimensional system of fields.)
Thus the blob complex is a natural generalization of something already
known to be interesting in higher homological degrees.
--- a/text/ncat.tex Thu Aug 11 12:50:50 2011 -0700
+++ b/text/ncat.tex Thu Aug 11 13:23:33 2011 -0700
@@ -1171,8 +1171,8 @@
\label{ex:blob-complexes-of-balls}
Fix an $n{-}k$-dimensional manifold $F$ and an $n$-dimensional system of fields $\cE$.
We will define an $A_\infty$ disk-like $k$-category $\cC$.
-When $X$ is a $m$-ball, with $m<k$, define $\cC(X) = \cE(X\times F)$.
-When $X$ is an $k$-ball,
+When $X$ is an $m$-ball, with $m<k$, define $\cC(X) = \cE(X\times F)$.
+When $X$ is a $k$-ball,
define $\cC(X; c) = \bc^\cE_*(X\times F; c)$
where $\bc^\cE_*$ denotes the blob complex based on $\cE$.
\end{example}
@@ -1283,7 +1283,7 @@
system of fields and local relations, followed by the usual TQFT definition of a
vector space invariant of manifolds given as Definition \ref{defn:TQFT-invariant}.
For an $A_\infty$ disk-like $n$-category, $\cl{\cC}$ is defined using a homotopy colimit instead.
-Recall that we can take a ordinary disk-like $n$-category $\cC$ and pass to the ``free resolution",
+Recall that we can take an ordinary disk-like $n$-category $\cC$ and pass to the ``free resolution",
an $A_\infty$ disk-like $n$-category $\bc_*(\cC)$, by computing the blob complex of balls
(recall Example \ref{ex:blob-complexes-of-balls} above).
We will show in Corollary \ref{cor:new-old} below that the homotopy colimit invariant
--- a/text/tqftreview.tex Thu Aug 11 12:50:50 2011 -0700
+++ b/text/tqftreview.tex Thu Aug 11 13:23:33 2011 -0700
@@ -51,7 +51,7 @@
The presentation here requires that the objects of $\cS$ have an underlying set,
but this could probably be avoided if desired.
-A $n$-dimensional {\it system of fields} in $\cS$
+An $n$-dimensional {\it system of fields} in $\cS$
is a collection of functors $\cC_k : \cM_k \to \Set$ for $0 \leq k \leq n$
together with some additional data and satisfying some additional conditions, all specified below.