#### 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
##### Publication
Revised: 17 December 2015
Accepted: 24 February 2016
Published: 10 February 2017
Proposed: David Gabai
Seconded: Jean-Pierre Otal, Martin Bridson
##### Authors
 Richard D Canary Department of Mathematics University of Michigan 2074 East Hall 530 Church St Ann Arbor, MI 48109-1043 United States Michelle Lee Department of Mathematics University of Maryland William E Kirwan Hall 4176 Campus Dr College Park, MD 20742-4015 United States Matthew Stover Department of Mathematics Temple University Wachman Hall 1805 N Broad St Philadelphia, PA 19122 United States Richard D Canary Michelle Lee Andrés Sambarino Faculté de Mathématiques Université Paris VI Pierre et Marie Curie 4 Place Jussieu 75005 Paris France Matthew Stover