Bredon Homology of Partition Complexes

Abstract

We prove that the Bredon homology or cohomology of the partition complex with fairly general coefficients is either trivial or computable in terms of constructions with the Steinberg module. The argument involves developing a theory of Bredon homology and cohomology approximation.

48 pages. Minor revisions. A typo in the statement of Corollary 1.2 was corrected, along with other typos. Some references have been added

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• The rank filtration via a filtered bar construction
• Bredon homology of wallpaper groups
• Symmetric Powers and Eilenberg--Maclane Spectra