Bounded cohomology of classifying spaces for families of subgroups

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--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.

v2: 20 pages, added Theorem 4.5, incorporated Section 6 into Section 4

References in corpus (2)

• On co-amenability for groups and von Neumann algebras
• Amenability and Acyclicity in Bounded Cohomology Theory

Cited by in corpus (3)

• Bounded cohomology and binate groups
• Median quasimorphisms on CAT(0) cube complexes and their cup products
• The space of non-extendable quasimorphisms