Equivariant Refinements

2013/08/13 by Adam Mole, Mole, Adam, Henrik Rueping +1
Mathematics · #18F25 (Primary) #19A31 #19B28 (Secondary) #55M10 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1308.2799

openalex publication_date 2013/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if an open cover of a finite dimensional space is equivariant with respect to some finite group action on the space then there is an equivariant refinement of bounded dimension. This will generalize some constructions of certain covers. Those generalizations play a key role in the proof of the Farrell-Jones conjecture for the general linear group over a finite field.

Related

• Equivariant covers for hyperbolic groups
• Equivariant classification of Gorenstein open log del Pezzo surfaces with finite group actions
• A genuine equivariant recognition principle for finite groups
• Recasting results in equivariant geometry: affine cosets, observable subgroups and existence of good quotients
• Equivariant birational geometry of linear actions