International Mathematics Research Notices ( IF 1.452 ) Pub Date : 2020-05-22 , DOI: 10.1093/imrn/rnaa088
Gregory Arone; W G Dwyer; Kathryn Lesh

We study Bredon homology approximations for spaces with an action of a compact Lie group G. We show that if M is a coMackey functor satisfying mild p-locality conditions, then Bredon homology of a G-space X with coefficients in M is determined by fixed points of p-toral subgroups of G acting on X. As an application we prove a vanishing result for the Bredon homology of the complex |${{\mathcal{L}}}_{n}$| of direct-sum decompositions of |${{\mathbb{C}}}^{n}$|⁠.

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