text/hochschild.tex
changeset 43 700ac2678d00
parent 39 5cf5940d1a2c
child 46 0ffcbbd8019c
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    95 We claim that
    95 We claim that
    96 \begin{thm}
    96 \begin{thm}
    97 The blob complex $\bc_*(S^1; C)$ on the circle is quasi-isomorphic to the
    97 The blob complex $\bc_*(S^1; C)$ on the circle is quasi-isomorphic to the
    98 usual Hochschild complex for $C$.
    98 usual Hochschild complex for $C$.
    99 \end{thm}
    99 \end{thm}
       
   100 
       
   101 \nn{Note that since both complexes are free (in particular, projective),
       
   102 quasi-isomorphic implies homotopy equivalent.  
       
   103 This applies to the two claims below also.
       
   104 Thanks to Peter Teichner for pointing this out to me.}
   100 
   105 
   101 This follows from two results. First, we see that
   106 This follows from two results. First, we see that
   102 \begin{lem}
   107 \begin{lem}
   103 \label{lem:module-blob}%
   108 \label{lem:module-blob}%
   104 The complex $K_*(C)$ (here $C$ is being thought of as a
   109 The complex $K_*(C)$ (here $C$ is being thought of as a