A characterization of relatively hyperbolic groups via bounded cohomology

Abstract

It was proved by Mineyev and Yaman that, if $(\Gamma ,{\Gamma }^{\prime })$ is a relatively hyperbolic pair, the comparison map $$H_b^k(\Gamma ,{\Gamma }^{\prime };V)\to H^k(\Gamma ,{\Gamma }^{\prime };V)$$ 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.

arXiv comment39 pp