text/intro.tex
changeset 962 87bfea2e3150
parent 937 6cfc2dc6ec6e
child 977 f5af4f863a8f
--- 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}),