
diff -r e0b304e6b975 -r e1d24be683bb text/basic_properties.tex
--- a/text/basic_properties.tex	Wed Oct 28 00:54:35 2009 +0000
+++ b/text/basic_properties.tex	Wed Oct 28 02:44:29 2009 +0000
@@ -27,7 +27,7 @@
 we have a splitting $s: H_0(\bc_*(B^n, c)) \to \bc_0(B^n; c)$
 of the quotient map
 $p: \bc_0(B^n; c) \to H_0(\bc_*(B^n, c))$.
-For example, this is always the case if you coefficient ring is a field.
+For example, this is always the case if the coefficient ring is a field.
 Then
 \begin{prop} \label{bcontract}
 For all $c \in \cC(\bd B^n)$ the natural map $p: \bc_*(B^n, c) \to H_0(\bc_*(B^n, c))$
@@ -66,14 +66,14 @@
 
 \begin{prop}
 For fixed fields ($n$-cat), $\bc_*$ is a functor from the category
-of $n$-manifolds and diffeomorphisms to the category of chain complexes and
+of $n$-manifolds and homeomorphisms to the category of chain complexes and
 (chain map) isomorphisms.
 \qed
 \end{prop}
 
 In particular,
 \begin{prop}  \label{diff0prop}
-There is an action of $\Diff(X)$ on $\bc_*(X)$.
+There is an action of $\Homeo(X)$ on $\bc_*(X)$.
 \qed
 \end{prop}
 
@@ -106,16 +106,16 @@
 The above map is very far from being an isomorphism, even on homology.
 This will be fixed in Section \ref{sec:gluing} below.
 
-\nn{Next para not need, since we already use bullet = gluing notation above(?)}
+%\nn{Next para not needed, since we already use bullet = gluing notation above(?)}
 
-An instance of gluing we will encounter frequently below is where $X = X_1 \du X_2$
-and $X\sgl = X_1 \cup_Y X_2$.
-(Typically one of $X_1$ or $X_2$ is a disjoint union of balls.)
-For $x_i \in \bc_*(X_i)$, we introduce the notation
-\eq{
-    x_1 \bullet x_2 \deq \gl(x_1 \otimes x_2) .
-}
-Note that we have resumed our habit of omitting boundary labels from the notation.
+%An instance of gluing we will encounter frequently below is where $X = X_1 \du X_2$
+%and $X\sgl = X_1 \cup_Y X_2$.
+%(Typically one of $X_1$ or $X_2$ is a disjoint union of balls.)
+%For $x_i \in \bc_*(X_i)$, we introduce the notation
+%\eq{
+%    x_1 \bullet x_2 \deq \gl(x_1 \otimes x_2) .
+%}
+%Note that we have resumed our habit of omitting boundary labels from the notation.
 
 
 




