On relatively hyperbolic groups
by
Asli Yaman
University of Bonn

We will discuss relative hyperbolicity, which is introduced by Gromov. Relatively hyperbolic groups can be understood as a generalisation both of Gromov hyperbolic groups and of geometrically finite Kleinian groups. We will present two equivalent definitions of relative hyperbolicity: a reformulation of the original definition of Gromov and a definition given by Bowditch, which characterises the notions by combinatoric means. We will also give another characterisation of relatively hyperbolic groups in terms of convergence groups. This latter characterisation allows to recognise relatively hyperbolic groups by the properties of their action on their boundaries and produces practical means to use them.

Date received: December 26, 2003