# HG changeset patch
# User kevin@6e1638ff-ae45-0410-89bd-df963105f760
# Date 1244663759 0
# Node ID 8ef65f3bea2bcb464cdf5b82292c66da7160a917
# Parent  0fb44b5068f5ac97f8b480ce1fbadc3c4c09ac61
small changes

diff -r 0fb44b5068f5 -r 8ef65f3bea2b blob1.tex
--- a/blob1.tex	Sun Jun 07 18:41:00 2009 +0000
+++ b/blob1.tex	Wed Jun 10 19:55:59 2009 +0000
@@ -25,6 +25,8 @@
 
 \versioninfo
 
+\noop{
+
 \section*{Todo}
 
 \subsection*{What else?...}
@@ -46,11 +48,8 @@
 \item dimension $n+1$ (generalized Deligne conjecture?)
 \item should be clear about PL vs Diff; probably PL is better
 (or maybe not)
-\item say what we mean by $n$-category, $A_\infty$ or $E_\infty$ $n$-category
 \item something about higher derived coend things (derived 2-coend, e.g.)
 \item shuffle product vs gluing product (?)
-\item commutative algebra results
-\item $A_\infty$ blob complex
 \item connection between $A_\infty$ operad and topological $A_\infty$ cat defs
 \end{itemize}
 \item lower priority
@@ -61,6 +60,7 @@
 \end{itemize}
 \end{itemize}
 
+} %end \noop
 
 \section{Introduction}
 
@@ -164,7 +164,9 @@
 
 \begin{property}[Skein modules]
 \label{property:skein-modules}%
-The $0$-th blob homology of $X$ is the usual skein module associated to $X$. (See \S \ref{sec:local-relations}.)
+The $0$-th blob homology of $X$ is the usual 
+(dual) TQFT Hilbert space (a.k.a.\ skein module) associated to $X$
+by $(\cF,\cU)$. (See \S \ref{sec:local-relations}.)
 \begin{equation*}
 H_0(\bc_*^{\cF,\cU}(X)) \iso A^{\cF,\cU}(X)
 \end{equation*}
@@ -198,8 +200,10 @@
             \bc_*(X_1) \otimes \bc_*(X_2) \ar[u]_{\gl_Y}
 }
 \end{equation*}
+\nn{should probably say something about associativity here (or not?)}
 \end{property}
 
+
 \begin{property}[Gluing formula]
 \label{property:gluing}%
 \mbox{}% <-- gets the indenting right
@@ -220,6 +224,8 @@
 \end{itemize}
 \end{property}
 
+\nn{add product formula?  $n$-dimensional fat graph operad stuff?}
+
 Properties \ref{property:functoriality}, \ref{property:gluing-map} and \ref{property:skein-modules} will be immediate from the definition given in
 \S \ref{sec:blob-definition}, and we'll recall them at the appropriate points there. \todo{Make sure this gets done.}
 Properties \ref{property:disjoint-union} and \ref{property:contractibility} are established in \S \ref{sec:basic-properties}.
diff -r 0fb44b5068f5 -r 8ef65f3bea2b text/A-infty.tex
--- a/text/A-infty.tex	Sun Jun 07 18:41:00 2009 +0000
+++ b/text/A-infty.tex	Wed Jun 10 19:55:59 2009 +0000
@@ -10,6 +10,9 @@
 \subsection{Topological $A_\infty$ categories}
 In this section we define a notion of `topological $A_\infty$ category' and sketch an equivalence with the usual definition of $A_\infty$ category. We then define `topological $A_\infty$ modules', and their morphisms and tensor products.
 
+\nn{And then we generalize all of this to $A_\infty$ $n$-categories [is this the
+best name for them?]}
+
 \begin{defn}
 \label{defn:topological-Ainfty-category}%
 A \emph{topological $A_\infty$ category} $\cC$ has a set of objects $\Obj(\cC)$, and for each interval $J$ and objects $a,b \in \Obj(\cC)$, a chain complex $\cC(J;a,b)$, along with
diff -r 0fb44b5068f5 -r 8ef65f3bea2b text/gluing.tex
--- a/text/gluing.tex	Sun Jun 07 18:41:00 2009 +0000
+++ b/text/gluing.tex	Wed Jun 10 19:55:59 2009 +0000
@@ -42,7 +42,8 @@
 \end{thm}
 
 Before proving this theorem, we embark upon a long string of definitions.
-For expository purposes, we begin with the $n=1$ special cases,\scott{Why are we treating the $n>1$ cases at all?} and define
+For expository purposes, we begin with the $n=1$ special cases,
+and define
 first topological $A_\infty$-algebras, then topological $A_\infty$-categories, and then topological $A_\infty$-modules over these. We then turn
 to the general $n$ case, defining topological $A_\infty$-$n$-categories and their modules.
 \nn{Something about duals?}