# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1318467000 25200
# Node ID 45ffa363a8c8009ba3a031391133e17b9ca4ce3d
# Parent  7afa2ffbbac8fb57a9775a5526714b1b2a7c48a4
a little more on operad action

diff -r 7afa2ffbbac8 -r 45ffa363a8c8 RefereeReport.pdf
Binary file RefereeReport.pdf has changed
diff -r 7afa2ffbbac8 -r 45ffa363a8c8 blob_changes_v3
--- a/blob_changes_v3	Wed Oct 12 15:10:54 2011 -0700
+++ b/blob_changes_v3	Wed Oct 12 17:50:00 2011 -0700
@@ -34,4 +34,5 @@
 - added remark about families of collar maps acting on the blob complex
 - small corrections to proof of product theorem (7.1.1)
 - added remarks that various homotopy equivalences we construct are well-defined up to a contractible set of choices
+- clarified that the surgery cylinder operad action is only up to coherent homotopy
 
diff -r 7afa2ffbbac8 -r 45ffa363a8c8 text/deligne.tex
--- a/text/deligne.tex	Wed Oct 12 15:10:54 2011 -0700
+++ b/text/deligne.tex	Wed Oct 12 17:50:00 2011 -0700
@@ -210,6 +210,9 @@
 When $k=0$, this coincides with the $C_*(\Homeo(M_0\to N_0))$ action of \S\ref{sec:evaluation}.
 \end{thm}
 
+The ``up to coherent homotopy" in the statement is due to the fact that the isomorphisms of 
+\ref{lem:bc-btc} and \ref{thm:gluing} are only defined to up to a contractible set of homotopies.
+
 If, in analogy to Hochschild cochains, we define elements of $\hom(M, N)$
 to be ``blob cochains", we can summarize the above proposition by saying that the $n$-SC operad acts on
 blob cochains.