--- a/text/definitions.tex	Wed Oct 28 00:54:35 2009 +0000
+++ b/text/definitions.tex	Wed Oct 28 02:44:29 2009 +0000
@@ -105,10 +105,21 @@
 covering $\bar{f}:Y\to Y$, then $f(c\times I) = \bar{f}(c)\times I$.
 \end{enumerate}
 
-\nn{need to introduce two notations for glued fields --- $x\bullet y$ and $x\sgl$}
+There are two notations we commonly use for gluing.
+One is 
+\[
+	x\sgl \deq \gl(x) \in \cC(X\sgl) , 
+\]
+for $x\in\cC(X)$.
+The other is
+\[
+	x_1\bullet x_2 \deq \gl(x_1\otimes x_2) \in \cC(X\sgl) , 
+\]
+in the case that $X = X_1 \du X_2$, with $x_i \in \cC(X_i)$.
 
-\bigskip
-Using the functoriality and $\bullet\times I$ properties above, together
+\medskip
+
+Using the functoriality and $\cdot\times I$ properties above, together
 with boundary collar homeomorphisms of manifolds, we can define the notion of 
 {\it extended isotopy}.
 Let $M$ be an $n$-manifold and $Y \subset \bd M$ be a codimension zero submanifold