# HG changeset patch # User kevin@6e1638ff-ae45-0410-89bd-df963105f760 # Date 1208801685 0 # Node ID 61751866cf69e2049932b478c3471cb28dc0c088 # Parent 8599e156a169f303d7ce6fd76f5b761c261b282f misc small edit(s) diff -r 8599e156a169 -r 61751866cf69 blob1.pdf Binary file blob1.pdf has changed diff -r 8599e156a169 -r 61751866cf69 blob1.tex --- a/blob1.tex Mon Apr 21 17:41:17 2008 +0000 +++ b/blob1.tex Mon Apr 21 18:14:45 2008 +0000 @@ -590,6 +590,8 @@ In this section we analyze the blob complex in dimension $n=1$ and find that for $S^1$ the homology of the blob complex is the Hochschild homology of the category (algebroid) that we started with. +\nn{or maybe say here that the complexes are quasi-isomorphic? in general, +should perhaps put more emphasis on the complexes and less on the homology.} Notation: $HB_i(X) = H_i(\bc_*(X))$. @@ -628,6 +630,8 @@ the boundary condition $c$ and the domains and ranges of the point labels. \item There is an evaluation map $e: \cC(I; a, b) \to \mor(a, b)$ given by composing the morphism labels of the points. +Note that we also need the * of *-1-category here in order to make all the morphisms point +the same way. \item For $x \in \mor(a, b)$ let $\chi(x) \in \cC(I; a, b)$ be the field with a single point (at some standard location) labeled by $x$. Then the kernel of the evaluation map $U(I; a, b)$ is generated by things of the