replacing "sort-of-simplicial" -> "cone-product", although I was rather fond of "sort-of-simplicial"; this isn't kvetching about your comment -- I was already planning on axing "sort-of-simplicial"
--- a/text/evmap.tex Mon Sep 20 06:10:49 2010 -0700
+++ b/text/evmap.tex Mon Sep 20 06:39:25 2010 -0700
@@ -21,9 +21,9 @@
introduce a homotopy equivalent alternate version of the blob complex, $\btc_*(X)$,
which is more amenable to this sort of action.
Recall from Remark \ref{blobsset-remark} that blob diagrams
-have the structure of a sort-of-simplicial set. \nn{need a more conventional sounding name: `polyhedral set'?}
+have the structure of a cone-product set.
Blob diagrams can also be equipped with a natural topology, which converts this
-sort-of-simplicial set into a sort-of-simplicial space.
+cone-product set into a cone-product space.
Taking singular chains of this space we get $\btc_*(X)$.
The details are in \S \ref{ss:alt-def}.
We also prove a useful result (Lemma \ref{small-blobs-b}) which says that we can assume that
@@ -216,7 +216,7 @@
\medskip
-Next we define the sort-of-simplicial space version of the blob complex, $\btc_*(X)$.
+Next we define the cone-product space version of the blob complex, $\btc_*(X)$.
First we must specify a topology on the set of $k$-blob diagrams, $\BD_k$.
We give $\BD_k$ the finest topology such that
\begin{itemize}
@@ -492,8 +492,8 @@
\nn{should comment at the start about any assumptions about smooth, PL etc.}
-\nn{should maybe mention alternate def of blob complex (sort-of-simplicial space instead of
-sort-of-simplicial set) where this action would be easy}
+\nn{should maybe mention alternate def of blob complex (cone-product space instead of
+cone-product set) where this action would be easy}
Let $CH_*(X, Y)$ denote $C_*(\Homeo(X \to Y))$, the singular chain complex of
the space of homeomorphisms