# HG changeset patch # User Kevin Walker # Date 1323736330 28800 # Node ID 87bfea2e3150996cd9055f359d5ca0f543afd352 # Parent c57afb230bb1d977db0c687a870343713bb7b602 added a homeo/pl/smooth etc note early in the intro diff -r c57afb230bb1 -r 87bfea2e3150 blob to-do --- a/blob to-do Mon Dec 12 15:01:37 2011 -0800 +++ b/blob to-do Mon Dec 12 16:32:10 2011 -0800 @@ -1,14 +1,13 @@ ====== big ====== -* add "homeomorphism" spiel before the first use of "homeomorphism" in the intro -* maybe also additional homeo warnings in other sections - -* Maybe give more details in 6.7.2 +[nothing!] ====== minor/optional ====== +* Maybe give more details in 6.7.2. Or maybe do this in some future paper. + [probably NO] * consider proving the gluing formula for higher codimension manifolds with morita equivalence diff -r c57afb230bb1 -r 87bfea2e3150 text/intro.tex --- a/text/intro.tex Mon Dec 12 15:01:37 2011 -0800 +++ b/text/intro.tex Mon Dec 12 16:32:10 2011 -0800 @@ -43,6 +43,16 @@ with sufficient limits and colimits would do. We could also replace many of our chain complexes with topological spaces (or indeed, work at the generality of model categories). +{\bf Note:} For simplicity, we will assume that all manifolds are unoriented and piecewise linear, unless stated otherwise. +In fact, all the results in this paper also hold for smooth manifolds, +as well as manifolds equipped with an orientation, spin structure, or $\mathrm{Pin}_\pm$ structure. +We will use ``homeomorphism" as a shorthand for ``piecewise linear homeomorphism". +The reader could also interpret ``homeomorphism" to mean an isomorphism in whatever category of manifolds we happen to +be working in (e.g.\ spin piecewise linear, oriented smooth, etc.). +In the smooth case there are additional technical details concerning corners and gluing +which we have omitted, since +most of the examples we are interested in require only a piecewise linear structure. + \subsection{Structure of the paper} The subsections of the introduction explain our motivations in defining the blob complex (see \S \ref{sec:motivations}),