--- a/text/appendixes/comparing_defs.tex Sun Mar 20 06:26:04 2011 -0700
+++ b/text/appendixes/comparing_defs.tex Wed Mar 23 15:19:37 2011 -0700
@@ -118,12 +118,12 @@
Each approach has advantages and disadvantages.
For better or worse, we choose bigons here.
-Define the $k$-morphisms $C^k$ of $C$ to be $\cC(B^k)_E$, where $B^k$ denotes the standard
+Define the $k$-morphisms $C^k$ of $C$ to be $\cC(B^k) \trans E$, where $B^k$ denotes the standard
$k$-ball, which we also think of as the standard bihedron (a.k.a.\ globe).
(For $k=1$ this is an interval, and for $k=2$ it is a bigon.)
Since we are thinking of $B^k$ as a bihedron, we have a standard decomposition of the $\bd B^k$
into two copies of $B^{k-1}$ which intersect along the ``equator" $E \cong S^{k-2}$.
-Recall that the subscript in $\cC(B^k)_E$ means that we consider the subset of $\cC(B^k)$
+Recall that the subscript in $\cC(B^k) \trans E$ means that we consider the subset of $\cC(B^k)$
whose boundary is splittable along $E$.
This allows us to define the domain and range of morphisms of $C$ using
boundary and restriction maps of $\cC$.