98 The above maps are compatible with the evaluation map actions of $C_*(\Diff(M))$.

    98 The above maps are compatible with the evaluation map actions of $C_*(\Diff(M))$.

    99 \end{prop}

    99 \end{prop}

   100 

   100 

   101 \begin{proof}

   101 \begin{proof}

   102 The actions agree in degree 0, and both are compatible with gluing.

   102 The actions agree in degree 0, and both are compatible with gluing.

   104 \end{proof}

   104 \end{proof}

   105 

   105 

   106 \medskip

   106 \medskip

   107 

   107 

   108 In view of Theorem \ref{thm:hochschild}, we have proved that $HH_*(k[t]) \cong C_*(\Sigma^\infty(S^1), k)$,

   108 In view of Theorem \ref{thm:hochschild}, we have proved that $HH_*(k[t]) \cong C_*(\Sigma^\infty(S^1), k)$,