Groups, Geometry, and Dynamics
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Published online: 2018-07-27
A characterization of relatively hyperbolic groups via bounded cohomologyFederico Franceschini (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