remove TOP; searched of "topological" and "PL" to find places where we mention TOP
--- a/text/appendixes/famodiff.tex Sun Sep 25 22:13:07 2011 -0600
+++ b/text/appendixes/famodiff.tex Sun Sep 25 22:31:22 2011 -0600
@@ -49,9 +49,9 @@
\end{enumerate}
\end{lemma}
-Note: We will prove a version of item 4 of Lemma \ref{basic_adaptation_lemma} for topological
-homeomorphisms in Lemma \ref{basic_adaptation_lemma_2} below.
-Since the proof is rather different we segregate it to a separate lemma.
+%Note: We will prove a version of item 4 of Lemma \ref{basic_adaptation_lemma} for topological
+%homeomorphisms in Lemma \ref{basic_adaptation_lemma_2} below.
+%Since the proof is rather different we segregate it to a separate lemma.
\begin{proof}
Our homotopy will have the form
@@ -221,6 +221,8 @@
% Edwards-Kirby: MR0283802
+\noop { %%%%%% begin \noop %%%%%%%%%%%%%%%%%%%%%%%
+
The above proof doesn't work for homeomorphisms which are merely continuous.
The $k=1$ case for plain, continuous homeomorphisms
is more or less equivalent to Corollary 1.3 of \cite{MR0283802}.
@@ -346,12 +348,12 @@
\end{proof}
-
+} %%%%%% end \noop %%%%%%%%%%%%%%%%%%%
\begin{lemma} \label{extension_lemma_c}
Let $\cX_*$ be any of $C_*(\Maps(X \to T))$ or singular chains on the
subspace of $\Maps(X\to T)$ consisting of immersions, diffeomorphisms,
-bi-Lipschitz homeomorphisms, PL homeomorphisms or plain old continuous homeomorphisms.
+bi-Lipschitz homeomorphisms, or PL homeomorphisms.
Let $G_* \subset \cX_*$ denote the chains adapted to an open cover $\cU$
of $X$.
Then $G_*$ is a strong deformation retract of $\cX_*$.
@@ -359,7 +361,7 @@
\begin{proof}
It suffices to show that given a generator $f:P\times X\to T$ of $\cX_k$ with
$\bd f \in G_{k-1}$ there exists $h\in \cX_{k+1}$ with $\bd h = f + g$ and $g \in G_k$.
-This is exactly what Lemma \ref{basic_adaptation_lemma} (or \ref{basic_adaptation_lemma_2})
+This is exactly what Lemma \ref{basic_adaptation_lemma}
gives us.
More specifically, let $\bd P = \sum Q_i$, with each $Q_i\in G_{k-1}$.
Let $F: I\times P\times X\to T$ be the homotopy constructed in Lemma \ref{basic_adaptation_lemma}.
--- a/text/intro.tex Sun Sep 25 22:13:07 2011 -0600
+++ b/text/intro.tex Sun Sep 25 22:31:22 2011 -0600
@@ -541,7 +541,7 @@
are equivalent to pivotal 2-categories, c.f. \S \ref{ssec:2-cats}.
Finally, we need a general name for isomorphisms between balls, where the balls could be
-piecewise linear or smooth or topological or Spin or framed or etc., or some combination thereof.
+piecewise linear or smooth or Spin or framed or etc., or some combination thereof.
We have chosen to use ``homeomorphism" for the appropriate sort of isomorphism, so the reader should
keep in mind that ``homeomorphism" could mean PL homeomorphism or diffeomorphism (and so on)
depending on context.
--- a/text/ncat.tex Sun Sep 25 22:13:07 2011 -0600
+++ b/text/ncat.tex Sun Sep 25 22:31:22 2011 -0600
@@ -84,7 +84,7 @@
We are being deliberately vague about what flavor of $k$-balls
we are considering.
They could be unoriented or oriented or Spin or $\mbox{Pin}_\pm$.
-They could be topological or PL or smooth.
+They could be PL or smooth.
%\nn{need to check whether this makes much difference}
(If smooth, ``homeomorphism" should be read ``diffeomorphism", and we would need
to be fussier about corners and boundaries.)
--- a/text/tqftreview.tex Sun Sep 25 22:13:07 2011 -0600
+++ b/text/tqftreview.tex Sun Sep 25 22:31:22 2011 -0600
@@ -42,7 +42,7 @@
unoriented PL manifolds of dimension
$k$ and morphisms homeomorphisms.
(We could equally well work with a different category of manifolds ---
-oriented, topological, smooth, spin, etc. --- but for simplicity we
+oriented, smooth, spin, etc. --- but for simplicity we
will stick with unoriented PL.)
Fix a symmetric monoidal category $\cS$.