# HG changeset patch # User Scott Morrison # Date 1318529758 14400 # Node ID 33404cea7dd3c601f59db1f4e78da650480bd20e # Parent fcd380e21e7cf3d93cc39555472b0d1ababcbf41 minor typos from recent edits diff -r fcd380e21e7c -r 33404cea7dd3 text/a_inf_blob.tex --- a/text/a_inf_blob.tex Thu Oct 13 10:54:06 2011 -0700 +++ b/text/a_inf_blob.tex Thu Oct 13 14:15:58 2011 -0400 @@ -271,7 +271,7 @@ or the fields $\cE(p^*(E))$, when $\dim(D) < k$. (Here $p^*(E)$ denotes the pull-back bundle over $D$.) Let $\cF_E$ denote this $k$-category over $Y$. -We can adapt the homotopy colimit construction (based decompositions of $Y$ into balls) to +We can adapt the homotopy colimit construction (based on decompositions of $Y$ into balls) to get a chain complex $\cl{\cF_E}(Y)$. \begin{thm} @@ -291,7 +291,7 @@ \[ \psi: \cl{\cF_E}(Y) \to \bc_*(E) . \] -0-simplices of the homotopy colimit $\cl{\cF_E}(Y)$ are glued up to give an element of $\bc_*(E)$. +The 0-simplices of the homotopy colimit $\cl{\cF_E}(Y)$ are glued up to give an element of $\bc_*(E)$. Simplices of positive degree are sent to zero. Let $G_* \sub \bc_*(E)$ be the image of $\psi$. diff -r fcd380e21e7c -r 33404cea7dd3 text/deligne.tex --- a/text/deligne.tex Thu Oct 13 10:54:06 2011 -0700 +++ b/text/deligne.tex Thu Oct 13 14:15:58 2011 -0400 @@ -211,7 +211,7 @@ \end{thm} The ``up to coherent homotopy" in the statement is due to the fact that the isomorphisms of -\ref{lem:bc-btc} and \ref{thm:gluing} are only defined to up to a contractible set of homotopies. +\ref{lem:bc-btc} and \ref{thm:gluing} are only defined up to a contractible set of homotopies. If, in analogy to Hochschild cochains, we define elements of $\hom(M, N)$ to be ``blob cochains", we can summarize the above proposition by saying that the $n$-SC operad acts on