diff -r e9ef2270eb61 -r 045e01f63729 text/blobdef.tex --- a/text/blobdef.tex Wed Jul 28 11:20:28 2010 -0700 +++ b/text/blobdef.tex Wed Jul 28 11:26:41 2010 -0700 @@ -67,7 +67,7 @@ just erasing the blob from the picture (but keeping the blob label $u$). -\nn{it seems rather strange to make this a theorem} +\nn{it seems rather strange to make this a theorem} \nn{it's a theorem because it's stated in the introduction, and I wanted everything there to have numbers that pointed into the paper --S} Note that directly from the definition we have \begin{thm} \label{thm:skein-modules} @@ -151,7 +151,7 @@ (This is necessary for Proposition \ref{blob-gluing}.) \end{itemize} Combining these two operations can give rise to configurations of blobs whose complement in $X$ is not -a manifold. \todo{example} +a manifold. Thus will need to be more careful when speaking of a field $r$ on the complement of the blobs. \begin{example} @@ -240,8 +240,8 @@ \end{itemize} For example, a diagram of $k$ strictly nested blobs corresponds to a $k$-simplex, while a diagram of $k$ disjoint blobs corresponds to a $k$-cube. -(This correspondence works best if we think of each twig label $u_i$ as having the form +(When the fields come from an $n$-category, this correspondence works best if we think of each twig label $u_i$ as having the form $x - s(e(x))$, where $x$ is an arbitrary field on $B_i$, $e: \cF(B_i) \to C$ is the evaluation map, -and $s:C \to \cF(B_i)$ is some fixed section of $e$. \todo{This parenthetical remark mysteriously specialises to the category case}) +and $s:C \to \cF(B_i)$ is some fixed section of $e$.)