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

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.