208 which satisfy the operad compatibility conditions, up to coherent homotopy.

   208 which satisfy the operad compatibility conditions, up to coherent homotopy.

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

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

   214 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

   215 blob cochains.

   218 blob cochains.

   216 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

   217 a higher dimensional version of the Deligne conjecture for Hochschild cochains and the little 2-disks operad.

   220 a higher dimensional version of the Deligne conjecture for Hochschild cochains and the little 2-disks operad.