# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1309796797 21600
# Node ID 40b2a6d891c6e14d8f9ac9c279fa818b78a998dc
# Parent  002b4838cc34726898daa96f9e399166ef785df7# Parent  c9b55efd79dda0489e5e59bbcf0c341f3e96e0cb
Automated merge with https://tqft.net/hg/blob/

diff -r 002b4838cc34 -r 40b2a6d891c6 blob_changes_v3
--- a/blob_changes_v3	Thu Jun 30 09:12:32 2011 -0700
+++ b/blob_changes_v3	Mon Jul 04 10:26:37 2011 -0600
@@ -27,7 +27,7 @@
 - added details to the construction of traditional 1-categories from disklike 1-categories (Appendix C.1)
 - extended the lemmas of Appendix B (about adapting families of homeomorphisms to open covers) to the topological category
 - modified families-of-homeomorphisms-action axiom for A-infinity n-categories, and added discussion of alternatives
-- added n-cat axiom for existence of splittings
+- added n-cat axiom for existence of splittings, and added similar axiom for fields
 - added transversality requirement to product morphism axiom
 - added remarks on Morita equivalence for n-categories
 - rewrote definition of colimit (in "From Balls to Manifolds" subsection) to allow for more general decompositions; also added more details
diff -r 002b4838cc34 -r 40b2a6d891c6 text/evmap.tex
--- a/text/evmap.tex	Thu Jun 30 09:12:32 2011 -0700
+++ b/text/evmap.tex	Mon Jul 04 10:26:37 2011 -0600
@@ -82,7 +82,7 @@
 \begin{proof}
 Since both complexes are free, it suffices to show that the inclusion induces
 an isomorphism of homotopy groups.
-To show that it suffices to show that for any finitely generated 
+To show this it in turn suffices to show that for any finitely generated 
 pair $(C_*, D_*)$, with $D_*$ a subcomplex of $C_*$ such that 
 \[
 	(C_*, D_*) \sub (\bc_*(X), \sbc_*(X))
diff -r 002b4838cc34 -r 40b2a6d891c6 text/tqftreview.tex
--- a/text/tqftreview.tex	Thu Jun 30 09:12:32 2011 -0700
+++ b/text/tqftreview.tex	Mon Jul 04 10:26:37 2011 -0600
@@ -192,6 +192,14 @@
 the gluing map is surjective.
 We say that fields in the image of the gluing map
 are transverse to $Y$ or splittable along $Y$.
+\item Splittings.
+Let $c\in \cC_k(X)$ and let $Y\sub X$ be a codimension 1 properly embedded submanifold of $X$.
+Then for most small perturbations of $Y$ (i.e.\ for an open dense
+subset of such perturbations) $c$ splits along $Y$.
+(In Example \ref{ex:maps-to-a-space(fields)}, $c$ splits along all such $Y$.
+In Example \ref{ex:traditional-n-categories(fields)}, $c$ splits along $Y$ so long as $Y$ 
+is in general position with respect to the cell decomposition
+associated to $c$.)
 \item Product fields.
 There are maps $\cC_{k-1}(Y) \to \cC_k(Y \times I)$, denoted
 $c \mapsto c\times I$.