Amalgam Anosov representations

摘要

Let Gamma be a one-ended, torsion-free hyperbolic group and let G be a semisimple Lie group with finite center. Using the canonical JSJ splitting due to Sela, we define amalgam Anosov representations of Gamma into G and prove that they form a domain of discontinuity for the action of Out(Gamma). In the appendix, we prove, using projective Anosov Schottky groups, that if the restriction of the representation to every Fuchsian or rigid vertex group of the JSJ splitting of Gamma is Anosov, with respect to a fixed pair of opposite parabolic subgroups, then rho is amalgam Anosov.