Relativizing characterizations of Anosov subgroups, I (with an appendix by Gregory A. Soifer)

We propose several common extensions of the classes of Anosov subgroups and geo- metrically finite Kleinian groups among discrete subgroups of semisimple Lie groups. We relativize various dynamical and coarse geometric characterizations of Anosov subgroups given in our earlier work, extending the class from intrinsically hyperbolic to relatively hyperbolic subgroups. We prove implications and equivalences between the various relativizations.