JournalsggdVol. 12, No. 3pp. 919–960

A characterization of relatively hyperbolic groups via bounded cohomology

  • Federico Franceschini

    Università di Pisa, Italy
A characterization of relatively hyperbolic groups via bounded cohomology cover
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Abstract

It was proved by Mineyev and Yaman that, if (Γ,Γ)(\Gamma, \Gamma') is a relatively hyperbolic pair, the comparison map

Hbk(Γ,Γ;V)\vtoHk(Γ,Γ;V)H_b^k(\Gamma, \Gamma'; V) \vto H^k(\Gamma, \Gamma'; V)

is surjective for every k2k \ge 2, and any bounded Γ\Gamma-module VV. By exploiting results of Groves and Manning, we give another proof of this result. Moreover, we prove the opposite implication under weaker hypotheses than the ones required by Mineyev and Yaman.

Cite this article

Federico Franceschini, A characterization of relatively hyperbolic groups via bounded cohomology. Groups Geom. Dyn. 12 (2018), no. 3, pp. 919–960

DOI 10.4171/GGD/463