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Groups, Geometry, and Dynamics

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Volume 12, Issue 3, 2018, pp. 919–960
DOI: 10.4171/GGD/463

Published online: 2018-07-27

A characterization of relatively hyperbolic groups via bounded cohomology

Federico Franceschini[1]

(1) Università di Pisa, Italy

It was proved by Mineyev and Yaman that, if $(\Gamma, \Gamma')$ is a relatively hyperbolic pair, the comparison map $$H_b^k(\Gamma, \Gamma'; V) \vto H^k(\Gamma, \Gamma'; V)$$ is surjective for every $k \ge 2$, and any bounded $\Gamma$-module $V$. 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.

Keywords: Relative bounded cohomology, relatively hyperbolic groups, Rips complex, comparison map, straightening

Franceschini Federico: A characterization of relatively hyperbolic groups via bounded cohomology. Groups Geom. Dyn. 12 (2018), 919-960. doi: 10.4171/GGD/463