Hyperbolicity and bounded-valued cohomology

Abstract

We generalise a theorem of Gersten on surjectivity of the restriction map in ℓ^∞-cohomology of groups. This leads to applications on subgroups of hyperbolic groups, quasi-isometric distinction of finitely generated groups and ℓ^∞-cohomology calculations for some well-known classes of groups. Along the way, we obtain hyperbolicity criteria for groups of type FP₂(Q) and for those satisfying a rational homological linear isoperimetric inequality, answering a question of Arora and Martínez-Pedroza.

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