The homotopy fixed points of the circle action on Hochschild homology

Abstract

We show that Connes' B-operator on a cyclic differential graded k-module M is a model for the canonical circle action on the geometric realization of M. This implies that the negative cyclic homology and the periodic cyclic homology of a differential graded category can be identified with the homotopy fixed points and the Tate fixed points of the circle action on its Hochschild complex.

v2: added a discussion of periodic cyclic homology

References in corpus (1)

• Higher Topos Theory

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