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Bounded cohomology of classifying spaces for families of subgroups

Kevin Li

Algebraic & Geometric Topology 23 (2023) 933–962
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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