Hochschild and cyclic homology are far from being homotopy functors
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- by S. Geller and C. Weibel PDF
- Proc. Amer. Math. Soc. 106 (1989), 49-57 Request permission
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 $H{P_*}(A)$.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 49-57
- MSC: Primary 18G30; Secondary 16A62, 18F25, 19D55
- DOI: https://doi.org/10.1090/S0002-9939-1989-0965242-0
- MathSciNet review: 965242