On a theorem of Eilenberg in simplicial Bredon-Illman cohomology with local coefficients

TL;DR

This paper proves a simplicial version of Eilenberg's classical theorem within equivariant cohomology and offers an alternative description of Bredon-Illman cohomology with local coefficients, facilitating spectral sequence derivation.

Contribution

It introduces a simplicial framework for Eilenberg's theorem in equivariant cohomology and provides a new perspective on Bredon-Illman cohomology with local coefficients.

Findings

Established a simplicial version of Eilenberg's theorem in equivariant cohomology.

Provided an alternative description of Bredon-Illman cohomology with local coefficients.

Derived a spectral sequence from the new cohomological framework.

Abstract

We prove simplicial version of a classical theorem of Eilenberg in the equivariant context and give an alternative description of the simplicial version of Bredon-Illman cohomology with local coefficients, as introduced in [15], to derive a spectral sequence.