equal
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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 |
397 is trivial at all but the topmost level. |
397 is trivial at levels 0 through $n-1$. |
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}. |