Reflexive homology

Daniel Graves

Published 2022-04-17Version 1

Reflexive homology is the homology theory associated to the reflexive crossed simplicial group. It is defined in terms of functor homology and is the most general way one can build an involution into Hochschild homology. In this paper we give a bicomplex for computing reflexive homology together with some calculations. We show that reflexive homology satisfies Morita invariance. We give a decomposition of the reflexive homology of a group algebra indexed by conjugacy classes of group elements, where the summands are defined in terms of a reflexive analogue of group homology. We prove that under nice conditions the involutive Hochschild homology studied by Braun and by Fern\`andez-Val\`encia and Giansiracusa coincides with reflexive homology.