text/hochschild.tex
changeset 314 6e23226d1cca
parent 286 ff867bfc8e9c
child 321 76c301fdf0a2
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   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