--- a/text/intro.tex Thu Apr 26 06:57:24 2012 -0600
+++ b/text/intro.tex Fri Apr 27 22:37:14 2012 -0700
@@ -191,7 +191,7 @@
It associates a bigraded vector space $A_{Kh}(W^4, L)$ to a 4-manifold $W$ together
with a link $L \subset \bd W$.
The original Khovanov homology of a link in $S^3$ is recovered as $A_{Kh}(B^4, L)$.
-%\todo{I'm tempted to replace $A_{Kh}$ with $\cl{Kh}$ throughout this page -S}
+%\todo{I'm tempted to replace $A_{Kh}$ with $\colimit{Kh}$ throughout this page -S}
How would we go about computing $A_{Kh}(W^4, L)$?
For the Khovanov homology of a link in $S^3$ the main tool is the exact triangle (long exact sequence)
@@ -415,7 +415,7 @@
There is a version of the blob complex for $\cC$ a disk-like $A_\infty$ $n$-category
instead of an ordinary $n$-category; this is described in \S \ref{sec:ainfblob}.
-The definition is in fact simpler, almost tautological, and we use a different notation, $\cl{\cC}(M)$.
+The definition is in fact simpler, almost tautological, and we use a different notation, $\colimit{\cC}(M)$.
The next theorem describes the blob complex for product manifolds
in terms of the $A_\infty$ blob complex of the disk-like $A_\infty$ $n$-categories constructed as in the previous example.
%The notation is intended to reflect the close parallel with the definition of the TQFT skein module via a colimit.
@@ -429,7 +429,7 @@
(see Example \ref{ex:blob-complexes-of-balls}).
Then
\[
- \bc_*(Y\times W; \cC) \simeq \cl{\bc_*(Y;\cC)}(W).
+ \bc_*(Y\times W; \cC) \simeq \colimit{\bc_*(Y;\cC)}(W).
\]
\end{thm:product}
The statement can be generalized to arbitrary fibre bundles, and indeed to arbitrary maps