blob: comparison pnas/pnas.tex

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 When $Y$ is a point this produces an $A_\infty$ $n$-category from a topological $n$-category,
 which can be thought of as a free resolution.
 \end{rem}
 This result is described in more detail as Example 6.2.8 of \cite{1009.5025}.
-%Fix a topological $n$-category $\cC$, which we'll now omit from notation.
+Fix a topological $n$-category $\cC$, which we'll now omit from notation.
-%Recall that for any $(n-1)$-manifold $Y$, the blob complex $\bc_*(Y)$ is naturally an $A_\infty$ category.
+Recall that for any $(n-1)$-manifold $Y$, the blob complex $\bc_*(Y)$ is naturally an $A_\infty$ category.
-The $A_\infty$ actions above allow us to state a gluing theorem.
-For simplicity, we omit the $n$-category $\cC$ from the notation.
 \begin{thm}[Gluing formula]
 \label{thm:gluing}
 \mbox{}% <-- gets the indenting right
 \begin{itemize}
 \bc_*(X\bigcup_Y \selfarrow) \simeq \bc_*(X) \Tensor^{A_\infty}_{\mathclap{\bc_*(Y)}} \selfarrow
 \end{equation*}
 \end{itemize}
 \end{thm}
+\begin{proof} (Sketch.)
+\end{proof}
 We next describe the blob complex for product manifolds, in terms of the $A_\infty$ blob complex of the $A_\infty$ $n$-categories constructed as above.
 \begin{thm}[Product formula]
 \label{thm:product}