added a homeo/pl/smooth etc note early in the intro
authorKevin Walker <kevin@canyon23.net>
Mon, 12 Dec 2011 16:32:10 -0800
changeset 962 87bfea2e3150
parent 961 c57afb230bb1
child 964 0dbaf072e916
added a homeo/pl/smooth etc note early in the intro
blob to-do
text/intro.tex
--- 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
 
--- 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}),