293 

   293 

   294 We define $g(C^j) = 0$ for $j > 0$.

   294 We define $g(C^j) = 0$ for $j > 0$.

   295 It is not hard to see that this defines a chain map from 

   295 It is not hard to see that this defines a chain map from 

   296 $\cB^\cT(M)$ to $C_*(\Maps(M\to T))$.

   296 $\cB^\cT(M)$ to $C_*(\Maps(M\to T))$.

   297 

   297 

   298 Next we show that $g$ induces a surjection on homology.

   301 Next we show that $g$ induces a surjection on homology.

   299 Fix $k > 0$ and choose an open cover $\cU$ of $M$ fine enough so that the union 

   302 Fix $k > 0$ and choose an open cover $\cU$ of $M$ fine enough so that the union 

   300 of any $k$ open sets of $\cU$ is contained in a disjoint union of balls in $M$.

   303 of any $k$ open sets of $\cU$ is contained in a disjoint union of balls in $M$.

   301 \nn{maybe should refer to elsewhere in this paper where we made a very similar argument}

   304 \nn{maybe should refer to elsewhere in this paper where we made a very similar argument}

   302 Let $S_*$ be the subcomplex of $C_*(\Maps(M\to T))$ generated by chains adapted to $\cU$.

   305 Let $S_*$ be the subcomplex of $C_*(\Maps(M\to T))$ generated by chains adapted to $\cU$.

   312 It follow that we can choose a decomposition $K$ of $M$ so that the support of $c$ is 

   315 It follow that we can choose a decomposition $K$ of $M$ so that the support of $c$ is 

   313 disjoint from the $n{-}1$-skeleton of $K$.

   316 disjoint from the $n{-}1$-skeleton of $K$.

   314 It is now easy to see that $c$ is in the image of $g$.

   317 It is now easy to see that $c$ is in the image of $g$.

   315 

   318 

   316 Next we show that $g$ is injective on homology.

   319 Next we show that $g$ is injective on homology.

   318 

   321 

   319 

   322 

   320 

   323 

   321 \nn{...}

   324 \nn{...}

   322 

   325