diff -r 4e4b6505d9ef -r 803cc581fd42 text/a_inf_blob.tex --- a/text/a_inf_blob.tex Sat Aug 28 17:34:20 2010 -0700 +++ b/text/a_inf_blob.tex Mon Aug 30 08:54:01 2010 -0700 @@ -288,26 +288,27 @@ or $M\to Y$, instead of an undecorated colimit with fancier $k$-categories over $Y$. Information about the specific map to $Y$ has been taken out of the categories and put into sphere modules and decorations. - -Let $F \to E \to Y$ be a fiber bundle as above. -Choose a decomposition $Y = \cup X_i$ -such that the restriction of $E$ to $X_i$ is a product $F\times X_i$. -\nn{resume revising here} -Choose the product structure (trivialization of the bundle restricted to $X_i$) as well. -To each codim-1 face $X_i\cap X_j$ we have a bimodule ($S^0$-module). -And more generally to each codim-$j$ face we have an $S^{j-1}$-module. -Decorate the decomposition with these modules and do the colimit. +\nn{...} - -\nn{There is a version of this last construction for arbitrary maps $E \to Y$ -(not necessarily a fibration). -In fact, there is also a version of the first construction for non-fibrations.} - - - -Note that Theorem \ref{thm:gluing} can be viewed as a special case of this one. -Let $X_1$ and $X_2$ be $n$-manifolds - +%Let $F \to E \to Y$ be a fiber bundle as above. +%Choose a decomposition $Y = \cup X_i$ +%such that the restriction of $E$ to $X_i$ is a product $F\times X_i$, +%and choose trivializations of these products as well. +% +%\nn{edit marker} +%To each codim-1 face $X_i\cap X_j$ we have a bimodule ($S^0$-module). +%And more generally to each codim-$j$ face we have an $S^{j-1}$-module. +%Decorate the decomposition with these modules and do the colimit. +% +% +%\nn{There is a version of this last construction for arbitrary maps $E \to Y$ +%(not necessarily a fibration).} +% +% +% +%Note that Theorem \ref{thm:gluing} can be viewed as a special case of this one. +%Let $X_1$ and $X_2$ be $n$-manifolds +% \subsection{A gluing theorem}