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

Group Theory;Geometric Topology