diff -r f5af4f863a8f -r a80cc9f9a65b text/intro.tex --- 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