A spectral sequence in Bredon cohomology

TL;DR

This paper introduces a spectral sequence framework for calculating Bredon cohomology of G-CW complexes, utilizing fixed point sets and local coefficients to facilitate computations across subgroup hierarchies.

Contribution

The paper constructs a novel spectral sequence for Bredon cohomology that leverages fixed point data and local coefficients, advancing computational methods in equivariant topology.

Findings

Spectral sequence converges to Bredon cohomology of G-CW complexes.

Provides a systematic approach to compute cohomology via fixed point sets.

Enhances understanding of the structure of Bredon cohomology in equivariant topology.

Abstract

For any finite group G, we construct a spectral sequence for computing the Bredon cohomology of a G-CW complex X, starting with the cohomology of X^H/\cup_{K>H}X^K with suitable local coefficients, for various H \leq G.