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}.