equal
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inserted
replaced
475 $\HC_*(M) \to K_*(M)$ |
475 $\HC_*(M) \to K_*(M)$ |
476 between the Hochschild complex and the blob complex (with bimodule point) |
476 between the Hochschild complex and the blob complex (with bimodule point) |
477 for degree $\le 2$. |
477 for degree $\le 2$. |
478 This map can be completed to a homotopy equivalence, though we will not prove that here. |
478 This map can be completed to a homotopy equivalence, though we will not prove that here. |
479 There are of course many such maps; what we describe here is one of the simpler possibilities. |
479 There are of course many such maps; what we describe here is one of the simpler possibilities. |
480 Describing the extension to higher degrees is straightforward but tedious. |
480 %Describing the extension to higher degrees is straightforward but tedious. |
481 \nn{but probably we should include the general case in a future version of this paper} |
481 %\nn{but probably we should include the general case in a future version of this paper} |
482 |
482 |
483 Recall that in low degrees $\HC_*(M)$ is |
483 Recall that in low degrees $\HC_*(M)$ is |
484 \[ |
484 \[ |
485 \cdots \stackrel{\bd}{\to} M \otimes C\otimes C \stackrel{\bd}{\to} |
485 \cdots \stackrel{\bd}{\to} M \otimes C\otimes C \stackrel{\bd}{\to} |
486 M \otimes C \stackrel{\bd}{\to} M |
486 M \otimes C \stackrel{\bd}{\to} M |