Abstract
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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.
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Keywords
bounded cohomology, Bredon cohomology, relative
amenability, relative hyperbolicity
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Mathematical Subject Classification
Primary: 20J06, 55N35
Secondary: 20F67, 43A07
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Publication
Received: 4 August 2021
Revised: 27 September 2021
Accepted: 7 November 2021
Published: 9 May 2023
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