# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1305345663 25200
# Node ID d8ae97449506d8d2a8307d23e149d19c92e537cc
# Parent  d75b7bfc44f265262ea6e4ac5e8867f91a7963cf# Parent  0a9adf027f479a52a632d49636e7b2a9f41b8cc2
merging by hand (?)

diff -r 0a9adf027f47 -r d8ae97449506 blob to-do
--- a/blob to-do	Fri May 13 20:52:18 2011 -0700
+++ b/blob to-do	Fri May 13 21:01:03 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
@@ -56,7 +53,7 @@
 
 * SCOTT: typo in delfig3a -- upper g should be g^{-1}
 
-* SCOTT: make sure acknowledge list doesn't omit anyone from blob seminar (I think I have all the speakers)
+* SCOTT: make sure acknowledge list doesn't omit anyone from blob seminar who should be included (I think I have all the speakers; does anyone other that the speakers rate a mention?)
 
 
 * review colors in figures
@@ -67,7 +64,8 @@
 
 * lemma [inject  6.3.5?] assumes more splittablity than the axioms imply (?)
 
+* consider putting conditions for enriched n-cat all in one place
+
 * SCOTT: figure for example 3.1.2 (sin 1/z)
 
 * SCOTT: add vertical arrow to middle of figure 19 (decomp poset)
-
diff -r 0a9adf027f47 -r d8ae97449506 blob_changes_v3
--- a/blob_changes_v3	Fri May 13 20:52:18 2011 -0700
+++ b/blob_changes_v3	Fri May 13 21:01:03 2011 -0700
@@ -5,11 +5,12 @@
 
 Also many typos corrected.
 
+
 The most significant changes are:
 
 - added to acknowledgements
 - clarified definition of splittable
-- change to pitchfork notation for splittable subsets of fields
+- changed to pitchfork notation for splittable subsets of fields
 - added definition of collaring homeomorphism
 - improved definition of bordism n-category
 - fixed definition of a refinement of a ball decomposition (intermediate manifolds should also be disjoint unions of balls)
diff -r 0a9adf027f47 -r d8ae97449506 text/ncat.tex
--- a/text/ncat.tex	Fri May 13 20:52:18 2011 -0700
+++ b/text/ncat.tex	Fri May 13 21:01:03 2011 -0700
@@ -1342,7 +1342,10 @@
 \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}
diff -r 0a9adf027f47 -r d8ae97449506 text/tqftreview.tex
--- a/text/tqftreview.tex	Fri May 13 20:52:18 2011 -0700
+++ b/text/tqftreview.tex	Fri May 13 21:01:03 2011 -0700
@@ -444,11 +444,13 @@
 The construction of the $n{+}1$-dimensional part of the theory (the path integral) 
 requires that the starting data (fields and local relations) satisfy additional
 conditions.
-We do not assume these conditions here, so when we say ``TQFT" we mean a decapitated TQFT
+(Specifically, $A(X; c)$ is finite dimensional for all $n$-manifolds $X$ and the inner products
+on $A(B^n; c)$ induced by the path integral of $B^{n+1}$ are positive definite for all $c$.)
+We do not assume these conditions here, so when we say ``TQFT" we mean a ``decapitated" TQFT
 that lacks its $n{+}1$-dimensional part. 
-Such a ``decapitated'' TQFT is sometimes also called an $n+\epsilon$ or 
-$n+\frac{1}{2}$ dimensional TQFT, referring to the fact that it assigns maps to $n{+}1$-dimensional
-mapping cylinders between $n$-manifolds, but nothing to arbitrary $n{+}1$-manifolds.
+Such a decapitated TQFT is sometimes also called an $n{+}\epsilon$ or 
+$n{+}\frac{1}{2}$ dimensional TQFT, referring to the fact that it assigns linear maps to $n{+}1$-dimensional
+mapping cylinders between $n$-manifolds, but nothing to general $n{+}1$-manifolds.
 
 Let $Y$ be an $n{-}1$-manifold.
 Define a linear 1-category $A(Y)$ as follows.