text/ncat.tex
changeset 774 b88c4c4af945
parent 773 775b5ca42bed
child 775 9ea10b1adfaa
--- 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*}