On the Rational Bredon Cohomology of Equivariant Configuration Spaces

2022/04/19 by Qiaofeng Zhu, Zhu, Qiaofeng
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2204.08719

openalex publication_date 2022/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• RO(G)-graded Bredon cohomology of Euclidean configuration spaces
• Representing Bredon cohomology with local coefficients
• C₂ equivariant characteristic classes over the rational Burnside ring
• An Eilenberg-Ganea Phenomenon for Actions with Virtually Cyclic Stabilisers
• Intermediaries in Bredon (Co)homology and Classifying Spaces