Bredon Homology of Partition Complexes

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 a theory of Bredon homology and cohomology approximation.

2010 Mathematics Subject Classification: 55N91, 55R40

Keywords and Phrases: homology approximations, equivariant approximations, Bredon homology, partition complexes

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