# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1305149533 25200
# Node ID 760cc71a0424e04e3465322ea917689cbe165196
# Parent  682fd0520c664425348068bf7ec7a85623a9b93d
add remarks to address the bizarre and inexplicable confusion about "hemisphere"

diff -r 682fd0520c66 -r 760cc71a0424 blob to-do
--- a/blob to-do	Wed May 11 14:20:10 2011 -0700
+++ b/blob to-do	Wed May 11 14:32:13 2011 -0700
@@ -15,9 +15,6 @@
 
 * Consider moving A_\infty stuff to a subsection
 
-* (?) dimension n+1, explain the statement and refer to KW's notes. [this was PT's suggestion, but it's sort of already in there.  do we need to do more?]
-	- add one more sentence: ~"finite dimensional and pos. def"
-
 * framings and duality -- work out what's going on! (alternatively, vague-ify current statement)
 
 * consider proving the gluing formula for higher codimension manifolds with
@@ -48,9 +45,6 @@
 
 modules:
 
-* Marked hemispheres, need better language.
-	- add something like "The is just a ball (\bd N \ N) with its entire boundary (\nd N) marked.  We use the term hemisphere because these balls are half the boundary of a larger ball.
-
 * Lemma 6.4.5 needs to actually construct this map! Needs more input! Do
 we actually need this as written?
 	- KW will look at it; probably needs to be weakened
diff -r 682fd0520c66 -r 760cc71a0424 text/ncat.tex
--- a/text/ncat.tex	Wed May 11 14:20:10 2011 -0700
+++ b/text/ncat.tex	Wed May 11 14:32:13 2011 -0700
@@ -1281,7 +1281,10 @@
 \caption{From manifold with boundary collar to marked ball}\label{blah15}\end{figure}
 
 Define the boundary of a marked $k$-ball $(B, N)$ to be the pair $(\bd B \setmin N, \bd N)$.
-Call such a thing a {marked $k{-}1$-hemisphere}.
+Call such a thing a {\it marked $k{-}1$-hemisphere}.
+(A marked $k{-}1$-hemisphere is, of course, just a $k{-}1$-ball with its entire boundary marked.
+We call it a hemisphere instead of a ball because it plays a role analogous
+to the $k{-}1$-spheres in the $n$-category definition.)
 
 \begin{lem}
 \label{lem:hemispheres}