Cohomological characterization of relative hyperbolicity and combination theorem

François Gautero (1) , Michael Heusener (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Domaines: Théorie des groupes [math.GR]

François Gautero, Michael Heusener. Cohomological characterization of relative hyperbolicity and combination theorem. Publicacions Matemàtiques, 2009, 53 (2), pp.489-514. ⟨hal-00425141⟩