--- a/text/deligne.tex	Tue Apr 19 15:52:37 2011 -0700
+++ b/text/deligne.tex	Sun Apr 24 13:55:58 2011 -0700
@@ -89,7 +89,8 @@
 cylinders.
 More specifically, we impose the following two equivalence relations:
 \begin{itemize}
-\item If $g: R_i\to R'_i$ is a homeomorphism, we can replace
+\item If $g: R_i\to R'_i$ is a homeomorphism which restricts to the identity on 
+$\bd R_i = \bd R'_i = E_0\cup \bd M_i$, we can replace
 \begin{eqnarray*}
 	(\ldots, R_{i-1}, R_i, R_{i+1}, \ldots) &\to& (\ldots, R_{i-1}, R'_i, R_{i+1}, \ldots) \\
 	(\ldots, f_{i-1}, f_i, \ldots) &\to& (\ldots, g\circ f_{i-1}, f_i\circ g^{-1}, \ldots),