209 On $C_0(SC^n_{\ol{M}\ol{N}})$ this agrees with the chain map $p$ defined above.

   209 On $C_0(SC^n_{\ol{M}\ol{N}})$ this agrees with the chain map $p$ defined above.

   210 When $k=0$, this coincides with the $C_*(\Homeo(M_0\to N_0))$ action of \S\ref{sec:evaluation}.

   210 When $k=0$, this coincides with the $C_*(\Homeo(M_0\to N_0))$ action of \S\ref{sec:evaluation}.

   211 \end{thm}

   211 \end{thm}

   212 

   212 

   213 The ``up to coherent homotopy" in the statement is due to the fact that the isomorphisms of 

   213 The ``up to coherent homotopy" in the statement is due to the fact that the isomorphisms of 

   215 

   215 

   216 If, in analogy to Hochschild cochains, we define elements of $\hom(M, N)$

   216 If, in analogy to Hochschild cochains, we define elements of $\hom(M, N)$

   217 to be ``blob cochains", we can summarize the above proposition by saying that the $n$-SC operad acts on

   217 to be ``blob cochains", we can summarize the above proposition by saying that the $n$-SC operad acts on

   218 blob cochains.

   218 blob cochains.

   219 As noted above, the $n$-SC operad contains the little $n{+}1$-balls operad, so this constitutes

   219 As noted above, the $n$-SC operad contains the little $n{+}1$-balls operad, so this constitutes