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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} |
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100 |
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101 \nn{Note that since both complexes are free (in particular, projective), |
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102 quasi-isomorphic implies homotopy equivalent. |
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103 This applies to the two claims below also. |
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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 |