392 Lurie has shown in \cite[Theorem 3.8.6]{0911.0018} that the topological chiral homology 

   392 Lurie has shown in \cite[Theorem 3.8.6]{0911.0018} that the topological chiral homology 

   393 of an $n$-manifold $M$ with coefficients in a certain $E_n$ algebra constructed from $T$ recovers 

   393 of an $n$-manifold $M$ with coefficients in a certain $E_n$ algebra constructed from $T$ recovers 

   394 the same space of singular chains on maps from $M$ to $T$, with the additional hypothesis that $T$ is $n-1$-connected.

   394 the same space of singular chains on maps from $M$ to $T$, with the additional hypothesis that $T$ is $n-1$-connected.

   395 This extra hypothesis is not surprising, in view of the idea described in Example \ref{ex:e-n-alg} 

   395 This extra hypothesis is not surprising, in view of the idea described in Example \ref{ex:e-n-alg} 

   396 that an $E_n$ algebra is roughly equivalent data to an $A_\infty$ $n$-category which 

   396 that an $E_n$ algebra is roughly equivalent data to an $A_\infty$ $n$-category which 

   398 Ricardo Andrade also told us about a similar result.

   398 Ricardo Andrade also told us about a similar result.

   399 \end{rem}

   399 \end{rem}

   400 

   400 

   401 \begin{proof}

   401 \begin{proof}

   402 The proof is again similar to that of Theorem \ref{thm:product}.

   402 The proof is again similar to that of Theorem \ref{thm:product}.