
diff -r 32e75ba211cd -r cf01e213044a text/hochschild.tex
--- a/text/hochschild.tex	Thu Apr 01 15:39:33 2010 -0700
+++ b/text/hochschild.tex	Tue Apr 06 08:43:37 2010 -0700
@@ -467,9 +467,6 @@
 \label{fig:hochschild-1-chains}
 \end{figure}
 
-In degree 2, we send $m\ot a \ot b$ to the sum of 24 ($=6\cdot4$) 2-blob diagrams as shown in
-Figure \ref{fig:hochschild-2-chains}. In Figure \ref{fig:hochschild-2-chains} the 1- and 2-blob diagrams are indicated only by their support.
-We leave it to the reader to determine the labels of the 1-blob diagrams.
 \begin{figure}[!ht]
 \begin{equation*}
 \mathfig{0.6}{hochschild/2-chains-0}
@@ -480,15 +477,6 @@
 \caption{The 0-, 1- and 2-chains in the image of $m \tensor a \tensor b$. Only the supports of the 1- and 2-blobs are shown.}
 \label{fig:hochschild-2-chains}
 \end{figure}
-Each 2-cell in the figure is labeled by a ball $V$ in $S^1$ which contains the support of all
-1-blob diagrams in its boundary.
-Such a 2-cell corresponds to a sum of the 2-blob diagrams obtained by adding $V$
-as an outer (non-twig) blob to each of the 1-blob diagrams in the boundary of the 2-cell.
-Figure \ref{fig:hochschild-example-2-cell} shows this explicitly for the 2-cell
-labeled $A$ in Figure \ref{fig:hochschild-2-chains}.
-Note that the (blob complex) boundary of this sum of 2-blob diagrams is
-precisely the sum of the 1-blob diagrams corresponding to the boundary of the 2-cell.
-(Compare with the proof of \ref{bcontract}.)
 
 \begin{figure}[!ht]
 \begin{equation*}
@@ -501,3 +489,16 @@
 \caption{One of the 2-cells from Figure \ref{fig:hochschild-2-chains}.}
 \label{fig:hochschild-example-2-cell}
 \end{figure}
+
+In degree 2, we send $m\ot a \ot b$ to the sum of 24 ($=6\cdot4$) 2-blob diagrams as shown in
+Figure \ref{fig:hochschild-2-chains}. In Figure \ref{fig:hochschild-2-chains} the 1- and 2-blob diagrams are indicated only by their support.
+We leave it to the reader to determine the labels of the 1-blob diagrams.
+Each 2-cell in the figure is labeled by a ball $V$ in $S^1$ which contains the support of all
+1-blob diagrams in its boundary.
+Such a 2-cell corresponds to a sum of the 2-blob diagrams obtained by adding $V$
+as an outer (non-twig) blob to each of the 1-blob diagrams in the boundary of the 2-cell.
+Figure \ref{fig:hochschild-example-2-cell} shows this explicitly for the 2-cell
+labeled $A$ in Figure \ref{fig:hochschild-2-chains}.
+Note that the (blob complex) boundary of this sum of 2-blob diagrams is
+precisely the sum of the 1-blob diagrams corresponding to the boundary of the 2-cell.
+(Compare with the proof of \ref{bcontract}.)




