Cohomological characterization of relative hyperbolicity and combination theorem

We give a cohomological characterization of Gromov relative hyperbolicity. As an application we prove a converse to the combination theorem for graphs of relatively hyperbolic groups given in a previous paper of the first author. We build upon, and follow the ideas of, the work of S. Gersten in ``Cohom. lower bounds for isoperim. funct. on groups’’ (Topology 37, 1998) about the same topics in the classical Gromov hyperbolic setting.