text/blobdef.tex
changeset 491 045e01f63729
parent 490 e9ef2270eb61
child 506 4a23163843a9
--- 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 $e$.)