diff -r 4d2dad357a49 -r c9f41c18a96f text/evmap.tex --- a/text/evmap.tex Tue Sep 21 07:37:41 2010 -0700 +++ b/text/evmap.tex Tue Sep 21 14:44:17 2010 -0700 @@ -191,7 +191,7 @@ and with $\supp(x_k) = U$. We can now take $d_j \deq \sum x_k$. It is clear that $\bd d_j = \sum (g_{j-1}(e_k) - g_j(e_k)) = g_{j-1}(s(\bd b)) - g_{j}(s(\bd b))$, as desired. -\nn{should maybe have figure} +\nn{should have figure} We now define \[ @@ -210,8 +210,6 @@ For sufficiently fine $\cV_{l-1}$ this will be possible. Since $C_*$ is finite, the process terminates after finitely many, say $r$, steps. We take $\cV_r = \cU$. - -\nn{should probably be more specific at the end} \end{proof} @@ -222,8 +220,6 @@ We give $\BD_k$ the finest topology such that \begin{itemize} \item For any $b\in \BD_k$ the action map $\Homeo(X) \to \BD_k$, $f \mapsto f(b)$ is continuous. -\item \nn{don't we need something for collaring maps?} -\nn{KW: no, I don't think so. not unless we wanted some extension of $CH_*$ to act} \item The gluing maps $\BD_k(M)\to \BD_k(M\sgl)$ are continuous. \item For balls $B$, the map $U(B) \to \BD_1(B)$, $u\mapsto (B, u, \emptyset)$, is continuous, where $U(B) \sub \bc_0(B)$ inherits its topology from $\bc_0(B)$ and the topology on @@ -418,7 +414,6 @@ We also will use the abbreviated notation $CH_*(X) \deq CH_*(X, X)$. (For convenience, we will permit the singular cells generating $CH_*(X, Y)$ to be more general than simplices --- they can be based on any cone-product polyhedron (see Remark \ref{blobsset-remark}).) -\nn{this note about our non-standard should probably go earlier in the paper, maybe intro} \begin{thm} \label{thm:CH} For $n$-manifolds $X$ and $Y$ there is a chain map