
diff -r fab3d057beeb -r 7afa2ffbbac8 text/deligne.tex
--- a/text/deligne.tex	Sat Oct 08 17:35:05 2011 -0700
+++ b/text/deligne.tex	Wed Oct 12 15:10:54 2011 -0700
@@ -205,7 +205,7 @@
 	C_*(SC^n_{\ol{M}\ol{N}})\otimes \hom(\bc_*(M_1), \bc_*(N_1))\otimes\cdots\otimes 
 \hom(\bc_*(M_{k}), \bc_*(N_{k})) \to  \hom(\bc_*(M_0), \bc_*(N_0))
 \]
-which satisfy the operad compatibility conditions.
+which satisfy the operad compatibility conditions, up to coherent homotopy.
 On $C_0(SC^n_{\ol{M}\ol{N}})$ this agrees with the chain map $p$ defined above.
 When $k=0$, this coincides with the $C_*(\Homeo(M_0\to N_0))$ action of \S\ref{sec:evaluation}.
 \end{thm}
@@ -228,7 +228,8 @@
 It suffices to show that the above maps are compatible with the relations whereby
 $SC^n_{\ol{M}\ol{N}}$ is constructed from the various $P$'s.
 This in turn follows easily from the fact that
-the actions of $C_*(\Homeo(\cdot\to\cdot))$ are local (compatible with gluing) and associative.
+the actions of $C_*(\Homeo(\cdot\to\cdot))$ are local (compatible with gluing) and associative
+(up to coherent homotopy).
 %\nn{should add some detail to above}
 \end{proof}
 




