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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hochschild and cyclic homology are far from being homotopy functors


Authors: S. Geller and C. Weibel
Journal: Proc. Amer. Math. Soc. 106 (1989), 49-57
MSC: Primary 18G30; Secondary 16A62, 18F25, 19D55
MathSciNet review: 965242
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Abstract: Given a homology theory $ {H_*}(A)$ on rings, based on a natural chain complex, one can form a new theory $ H_*^h(A)$ which is universal with respect to the homotopy property $ {H_*}(A) \simeq {H_*}(A[t])$. We show that the homotopy theories $ HH_*^h$ and $ HC_*^h$ associated to Hochschild and cyclic homology are both zero. On the other hand, if $ HC_*^ - $ denotes Goodwillie's variant of cyclic homology, and $ A$ contains a field of characteristic 0, we show that $ (H{C^ - })_*^hA$ is Connes' periodic cyclic homology $ H{P_*}(A)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0965242-0
PII: S 0002-9939(1989)0965242-0
Keywords: Hochschild homology, cyclic homology, homotopy functor, Moore complex
Article copyright: © Copyright 1989 American Mathematical Society