Bounded cohomology of classifying spaces for families of subgroups

Li, Kevin

doi:10.2140/agt.2023.23.933

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Bounded cohomology of classifying spaces for families of subgroups

Kevin Li

Algebraic & Geometric Topology 23 (2023) 933–962

DOI: 10.2140/agt.2023.23.933

Abstract

We introduce a bounded version of Bredon cohomology for groups relative to a family of subgroups. Our theory generalizes bounded cohomology and differs from Mineyev and Yaman’s relative bounded cohomology for pairs. We obtain cohomological characterizations of relative amenability and relative hyperbolicity, analogous to the results of Johnson and Mineyev for bounded cohomology.

Keywords

bounded cohomology, Bredon cohomology, relative amenability, relative hyperbolicity

Mathematical Subject Classification

Primary: 20J06, 55N35

Secondary: 20F67, 43A07

References

Publication

Received: 4 August 2021

Revised: 27 September 2021

Accepted: 7 November 2021

Published: 9 May 2023

Authors

Kevin Li
School of Mathematical Sciences University of Southampton Southampton United Kingdom	Fakultät für Mathematik Universität Regensburg Regensburg Germany

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Volume 23, issue 2 (2023)