Volume 21, issue 1 (2017)

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Amalgam Anosov representations

Appendix: Richard D Canary, Michelle Lee, Andrés Sambarino and Matthew Stover

Geometry & Topology 21 (2017) 215–251
Abstract

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 $Out\left(\Gamma \right)$. 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.

Keywords
character variety, Anosov representation, hyperbolic groups
Mathematical Subject Classification 2010
Primary: 20H10, 22E40, 57M50