398 The blob complex for $M$ with coefficients in the fundamental $A_\infty$ $n$-category for $T$ 

   398 The blob complex for $M$ with coefficients in the fundamental $A_\infty$ $n$-category for $T$ 

   399 is quasi-isomorphic to singular chains on maps from $M$ to $T$.

   399 is quasi-isomorphic to singular chains on maps from $M$ to $T$.

   400 $$\cB^\cT(M) \simeq C_*(\Maps(M\to T)).$$

   400 $$\cB^\cT(M) \simeq C_*(\Maps(M\to T)).$$

   401 \end{thm}

   401 \end{thm}

   402 \begin{rem}

   402 \begin{rem}

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

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

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

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

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

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

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

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

   408 is trivial at levels 0 through $n-1$.

   408 is trivial at levels 0 through $n-1$.