--- a/text/ncat.tex Sun May 08 09:05:53 2011 -0700
+++ b/text/ncat.tex Sun May 08 22:08:47 2011 -0700
@@ -192,7 +192,7 @@
becomes a normal product.)
\end{lem}
-\begin{figure}[!ht] \centering
+\begin{figure}[t] \centering
\begin{tikzpicture}[%every label/.style={green}
]
\node[fill=black, circle, label=below:$E$, inner sep=1.5pt](S) at (0,0) {};
@@ -264,7 +264,7 @@
(For $k=n$ in the ordinary (non-$A_\infty$) case, see below.)
\end{axiom}
-\begin{figure}[!ht] \centering
+\begin{figure}[t] \centering
\begin{tikzpicture}[%every label/.style={green},
x=1.5cm,y=1.5cm]
\node[fill=black, circle, label=below:$E$, inner sep=2pt](S) at (0,0) {};
@@ -285,7 +285,7 @@
any sequence of gluings (in the sense of Definition \ref{defn:gluing-decomposition}, where all the intermediate steps are also disjoint unions of balls) yields the same result.
\end{axiom}
-\begin{figure}[!ht]
+\begin{figure}[t]
$$\mathfig{.65}{ncat/strict-associativity}$$
\caption{An example of strict associativity.}\label{blah6}\end{figure}
@@ -323,7 +323,7 @@
and these various $m$-fold composition maps satisfy an
operad-type strict associativity condition (Figure \ref{fig:operad-composition}).}
-\begin{figure}[!ht]
+\begin{figure}[t]
$$\mathfig{.8}{ncat/operad-composition}$$
\caption{Operad composition and associativity}\label{fig:operad-composition}\end{figure}
@@ -588,7 +588,7 @@
a & \mapsto & s_{Y,J}(a \cup ((a|_Y)\times J)) .
\end{eqnarray*}
(See Figure \ref{glue-collar}.)
-\begin{figure}[!ht]
+\begin{figure}[t]
\begin{equation*}
\begin{tikzpicture}
\def\rad{1}
@@ -837,7 +837,7 @@
\end{example}
-\begin{example}[The bordism $n$-category of $d$-manifolds, ordinary version]
+\begin{example}[te bordism $n$-category of $d$-manifolds, ordinary version]
\label{ex:bord-cat}
\rm
\label{ex:bordism-category}
@@ -912,7 +912,7 @@
linear combinations of connected components of $T$, and the local relations are trivial.
There's no way for the blob complex to magically recover all the data of $\pi^\infty_{\leq 0}(T) \iso C_* T$.
-\begin{example}[The bordism $n$-category of $d$-manifolds, $A_\infty$ version]
+\begin{example}[te bordism $n$-category of $d$-manifolds, $A_\infty$ version]
\rm
\label{ex:bordism-category-ainf}
As in Example \ref{ex:bord-cat}, for $X$ a $k$-ball, $k<n$, we define $\Bord^{n,d}_\infty(X)$
@@ -1045,7 +1045,7 @@
See Figure \ref{partofJfig} for an example.
\end{defn}
-\begin{figure}[!ht]
+\begin{figure}[t]
\begin{equation*}
\mathfig{.63}{ncat/zz2}
\end{equation*}
@@ -1276,7 +1276,7 @@
%(If $\cD$ were a general TQFT, we would define $\cM(B, N)$ to be
%the subset of $\cD((B\times \bd W)\cup (N\times W))$ which is splittable along $N\times \bd W$.)
-\begin{figure}[!ht]
+\begin{figure}[t]
$$\mathfig{.55}{ncat/boundary-collar}$$
\caption{From manifold with boundary collar to marked ball}\label{blah15}\end{figure}
@@ -1342,7 +1342,7 @@
of splitting a marked $k$-ball into two (marked or plain) $k$-balls.
(See Figure \ref{zzz3}.)
-\begin{figure}[!ht]
+\begin{figure}[t]
\begin{equation*}
\mathfig{.4}{ncat/zz3}
\end{equation*}
@@ -1405,7 +1405,7 @@
action maps and $n$-category composition.
See Figure \ref{zzz1b}.
-\begin{figure}[!ht]
+\begin{figure}[t]
\begin{equation*}
\mathfig{0.49}{ncat/zz0} \mathfig{0.49}{ncat/zz1}
\end{equation*}