# HG changeset patch
# User Scott Morrison <scott@tqft.net>
# Date 1323746817 28800
# Node ID 0dbaf072e9162e43cd30cc08913980b93c7cf40f
# Parent  87bfea2e3150996cd9055f359d5ca0f543afd352# Parent  d875a8378d83468683f0c3b5fd21cd4f62eb1d24
Automated merge with https://tqft.net/hg/blob

diff -r d875a8378d83 -r 0dbaf072e916 blob to-do
--- a/blob to-do	Mon Dec 12 19:26:44 2011 -0800
+++ b/blob to-do	Mon Dec 12 19:26:57 2011 -0800
@@ -1,16 +1,13 @@
 
 ====== big ======
 
-* add "homeomorphism" spiel befure the first use of "homeomorphism in the intro
-* maybe also additional homeo warnings in other sections
-
-* Lemma 3.2.3 (\ref{support-shrink}) implicitly assumes embedded (non-self-intersecting) blobs. this can be fixed, of course, but it makes the argument more difficult to understand
-
-* Maybe give more details in 6.7.2
+[nothing!]
 
 
 ====== minor/optional ======
 
+* Maybe give more details in 6.7.2.  Or maybe do this in some future paper.
+
 [probably NO] * consider proving the gluing formula for higher codimension manifolds with
 morita equivalence
 
diff -r d875a8378d83 -r 0dbaf072e916 text/basic_properties.tex
--- a/text/basic_properties.tex	Mon Dec 12 19:26:44 2011 -0800
+++ b/text/basic_properties.tex	Mon Dec 12 19:26:57 2011 -0800
@@ -74,6 +74,9 @@
 For $y \in \bc_*(X)$ with $y = \sum c_i b_i$ ($c_i$ a non-zero number, $b_i$ a blob diagram),
 we define $\supp(y) \deq \bigcup_i \supp(b_i)$.
 
+%%%%% the following is true in spirit, but technically incorrect if blobs are not embedded; 
+%%%%% we only use this once, so move lemma and proof to Hochschild section
+\noop{ %%%%%%%%%% begin \noop
 For future use we prove the following lemma.
 
 \begin{lemma} \label{support-shrink}
@@ -94,6 +97,7 @@
 Both $f$ and the identity are compatible with $T$ (in the sense of acyclic models, \S\ref{sec:moam}), 
 so $f$ and the identity map are homotopic.
 \end{proof}
+} %%%%%%%%%%%%% end \noop
 
 For the next proposition we will temporarily restore $n$-manifold boundary
 conditions to the notation. Let $X$ be an $n$-manifold, with $\bd X = Y \cup Y \cup Z$.
diff -r d875a8378d83 -r 0dbaf072e916 text/hochschild.tex
--- a/text/hochschild.tex	Mon Dec 12 19:26:44 2011 -0800
+++ b/text/hochschild.tex	Mon Dec 12 19:26:57 2011 -0800
@@ -218,7 +218,10 @@
 to distance $\ep$ from *.
 (Move right or left so as to shrink the blob.)
 Extend to get a chain map $f: F_*^\ep \to F_*^\ep$.
-By Lemma \ref{support-shrink}, $f$ is homotopic to the identity.
+By Corollary \ref{disj-union-contract}, 
+$f$ is homotopic to the identity.
+(Use the facts that $f$ factors though a map from a disjoint union of balls
+into $S^1$, and that $f$ is the identity in degree 0.)
 Since the image of $f$ is in $J_*$, and since any blob chain is in $F_*^\ep$
 for $\ep$ sufficiently small, we have that $J_*$ is homotopic to all of $\bc_*(S^1)$.
 
diff -r d875a8378d83 -r 0dbaf072e916 text/intro.tex
--- a/text/intro.tex	Mon Dec 12 19:26:44 2011 -0800
+++ b/text/intro.tex	Mon Dec 12 19:26:57 2011 -0800
@@ -43,6 +43,16 @@
 with sufficient limits and colimits would do.
 We could also replace many of our chain complexes with topological spaces (or indeed, work at the generality of model categories).
 
+{\bf Note:} For simplicity, we will assume that all manifolds are unoriented and piecewise linear, unless stated otherwise.
+In fact, all the results in this paper also hold for smooth manifolds, 
+as well as manifolds equipped with an orientation, spin structure, or $\mathrm{Pin}_\pm$ structure.  
+We will use ``homeomorphism" as a shorthand for ``piecewise linear homeomorphism".
+The reader could also interpret ``homeomorphism" to mean an isomorphism in whatever category of manifolds we happen to 
+be working in (e.g.\ spin piecewise linear, oriented smooth, etc.).
+In the smooth case there are additional technical details concerning corners and gluing 
+which we have omitted, since 
+most of the examples we are interested in require only a piecewise linear structure.
+
 
 \subsection{Structure of the paper}
 The subsections of the introduction explain our motivations in defining the blob complex (see \S \ref{sec:motivations}),