Cohomological Characterization of Relative Hyperbolicity and Combination Theorem

Abstract

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 F. Gautero, "Geodesics in trees of hyperbolic and relatively hyperbolic groups," Preprint. We build upon and follow the ideas of the work of S. M. Gersten about the same topics in the classical Gromov hyperbolic setting.