
diff -r ea5d8fbcd5bc -r 1a52d23b9719 text/evmap.tex
--- a/text/evmap.tex	Mon Jul 13 20:22:21 2009 +0000
+++ b/text/evmap.tex	Fri Jul 17 19:40:05 2009 +0000
@@ -481,8 +481,27 @@
 \medskip
 
 
+\hrule\medskip\hrule\medskip
+
+\nn{outline of what remains to be done:}
+
+\begin{itemize}
+\item We need to assemble the maps for the various $G^{i,m}$ into
+a map for all of $CD_*\ot \bc_*$.
+One idea: Think of the $g_j$ as a sort of homotopy (from $CD_*\ot \bc_*$ to itself) 
+parameterized by $[0,\infty)$.  For each $p\ot b$ in $CD_*\ot \bc_*$ choose a sufficiently
+large $j'$.  Use these choices to reparameterize $g_\bullet$ so that each
+$p\ot b$ gets pushed as far as the corresponding $j'$.
+\item Independence of metric, $\ep_i$, $\delta_i$:
+For a different metric etc. let $\hat{G}^{i,m}$ denote the alternate subcomplexes
+and $\hat{N}_{i,l}$ the alternate neighborhoods.
+Main idea is that for all $i$ there exists sufficiently large $k$ such that
+$\hat{N}_{k,l} \sub N_{i,l}$, and similarly with the roles of $N$ and $\hat{N}$ reversed.
+\item Also need to prove associativity.
+\end{itemize}
 
 
+\nn{to be continued....}
 
 \noop{
 
@@ -497,7 +516,6 @@
 }
 
 
-\nn{to be continued....}
 
 
 %\nn{say something about associativity here}




