--- a/blob to-do	Sun May 08 09:05:53 2011 -0700
+++ b/blob to-do	Sun May 08 22:08:47 2011 -0700
@@ -65,4 +65,7 @@
 
 * ? define Morita equivalence?
 
-* maybe put most figures at top of page
\ No newline at end of file
+* number equations in same sequence as everything else
+
+* make sure we are clear that boundary = germ
+

--- a/text/a_inf_blob.tex	Sun May 08 09:05:53 2011 -0700
+++ b/text/a_inf_blob.tex	Sun May 08 22:08:47 2011 -0700
@@ -400,7 +400,7 @@
 $$\cB^\cT(M) \simeq C_*(\Maps(M\to T)).$$
 \end{thm}
 \begin{rem}
-Lurie has shown in \cite[Theorem 3.8.6]{0911.0018} that the topological chiral homology 
+Lurie has shown in \cite[teorem 3.8.6]{0911.0018} that the topological chiral homology 
 of an $n$-manifold $M$ with coefficients in a certain $E_n$ algebra constructed from $T$ recovers 
 the same space of singular chains on maps from $M$ to $T$, with the additional hypothesis that $T$ is $n-1$-connected.
 This extra hypothesis is not surprising, in view of the idea described in Example \ref{ex:e-n-alg} 

--- a/text/hochschild.tex	Sun May 08 09:05:53 2011 -0700
+++ b/text/hochschild.tex	Sun May 08 22:08:47 2011 -0700
@@ -537,7 +537,7 @@
 In degree 1, we send $m\ot a$ to the sum of two 1-blob diagrams
 as shown in Figure \ref{fig:hochschild-1-chains}.
 
-\begin{figure}[ht]
+\begin{figure}[t]
 \begin{equation*}
 \mathfig{0.4}{hochschild/1-chains}
 \end{equation*}
@@ -548,14 +548,14 @@
 \label{fig:hochschild-1-chains}
 \end{figure}
 
-\begin{figure}[ht]
+\begin{figure}[t]
 \begin{equation*}
 \mathfig{0.6}{hochschild/2-chains-0}
 \end{equation*}
 \caption{The 0-chains in the image of $m \tensor a \tensor b$.}
 \label{fig:hochschild-2-chains-0}
 \end{figure}
-\begin{figure}[ht]
+\begin{figure}[t]
 \begin{equation*}
 \mathfig{0.4}{hochschild/2-chains-1} \qquad \mathfig{0.4}{hochschild/2-chains-2}
 \end{equation*}
@@ -564,7 +564,7 @@
 \label{fig:hochschild-2-chains-12}
 \end{figure}
 
-\begin{figure}[ht]
+\begin{figure}[t]
 \begin{equation*}
 A = \mathfig{0.1}{hochschild/v_1} + \mathfig{0.1}{hochschild/v_2} + \mathfig{0.1}{hochschild/v_3} + \mathfig{0.1}{hochschild/v_4}
 \end{equation*}

--- a/text/intro.tex	Sun May 08 09:05:53 2011 -0700
+++ b/text/intro.tex	Sun May 08 22:08:47 2011 -0700
@@ -98,7 +98,7 @@
 
 \tikzstyle{box} = [rectangle, rounded corners, draw,outer sep = 5pt, inner sep = 5pt, line width=0.5pt]
 
-\begin{figure}[!ht]
+\begin{figure}[t]
 {\center
 \beginpgfgraphicnamed{gadgets-external}%
 \begin{tikzpicture}[align=center,line width = 1.5pt]

--- 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*}

--- a/text/obsolete/explicit.tex	Sun May 08 09:05:53 2011 -0700
+++ b/text/obsolete/explicit.tex	Sun May 08 22:08:47 2011 -0700
@@ -45,7 +45,7 @@
 so we conclude that for a fixed $p$, $\partial_p H''(1,p,x) = 0$ for all $x$ outside the union of $k$ open sets from the open cover, namely
 $\bigcup_{i=1}^k U_{l_i}$ where for each $i$, we choose $l_i$ so $\frac{l_i -1}{L} \leq p_i \leq \frac{l_i}{L}$. It may be helpful to refer to Figure \ref{fig:supports}.
 
-\begin{figure}[!ht]
+\begin{figure}[t]
 \begin{equation*}
 \mathfig{0.5}{explicit/supports}
 \end{equation*}
@@ -65,7 +65,7 @@
 \end{align*}
 (Note that we're abusing notation somewhat, using the fact that $u''(t,p,x)_i$ depends on $p$ only through $p_i$.)
 To see what's going on here, it may be helpful to look at Figure \ref{fig:supports_4}, which shows the support of $\partial_p u'(1,p,x)$.
-\begin{figure}[!ht]
+\begin{figure}[t]
 \begin{equation*}
 \mathfig{0.4}{explicit/supports_4} \qquad \qquad \mathfig{0.4}{explicit/supports_36}
 \end{equation*}

--- a/text/obsolete/smallblobs.tex	Sun May 08 09:05:53 2011 -0700
+++ b/text/obsolete/smallblobs.tex	Sun May 08 22:08:47 2011 -0700
@@ -117,7 +117,7 @@
 As in the $k=1$ case, the first term, corresponding to $i(b) = \eset$, makes the all balls in $\beta$ $\cV_1$-small. However, if this were the only term $s$ would not be a chain map, because we have no control over $\restrict{\phi_{\beta}}{x_0 = 0}(\bdy b)$. This necessitates the other terms, which fix the boundary at successively higher codimensions.
 
 It may be useful to look at Figure \ref{fig:erectly-a-tent-badly} to help understand the arrangement. The red, blue and orange $2$-cells there correspond to the $m=0$, $m=1$ and $m=2$ terms respectively, while the $3$-cells (only one of each type is shown) correspond to the terms in the homotopy $h$.
-\begin{figure}[!ht]
+\begin{figure}[t]
 $$\mathfig{0.5}{smallblobs/tent}$$
 \caption{``Erecting a tent badly.'' We know where we want to send a simplex, and each of the iterated boundary components. However, these do not agree, and we need to stitch the pieces together. Note that these diagrams don't exactly match the situation in the text: a $k$-simplex has $k+1$ boundary components, while a $k$-blob has $k$ boundary terms.}
 \label{fig:erectly-a-tent-badly}