On the Rational Bredon Cohomology of Equivariant Configuration Spaces

TL;DR

This paper investigates the Bredon cohomology of equivariant configuration spaces under group actions, providing a decomposition of homology systems and computing rational cohomology for specific nonabelian groups.

Contribution

It introduces a decomposition method for the homology Bredon coefficient system of configuration spaces with group actions and computes their rational Bredon cohomology for certain nonabelian groups.

Findings

Decomposition of homology Bredon coefficient systems

Explicit rational Bredon cohomology calculations for small nonabelian groups

Enhanced understanding of equivariant configuration spaces

Abstract

Bredon cohomology is a cohomology theory that applies to topological spaces equipped with the group actions. For any group G, given a real linear representation V , the configuration space of V has a natural diagonal G-action. In the paper we study this group action on the configuration space and give a decomposition of the homology Bredon coefficient system of the configuration space and apply this to compute rational Bredon cohomology of the configuration space for small nonabelian group G.