Amalgam Anosov representations

Canary, Richard¹ ; Lee, Michelle² ; Stover, Matthew³

¹ Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church St, Ann Arbor, MI 48109-1043, United States
² Department of Mathematics, University of Maryland, William E Kirwan Hall, 4176 Campus Dr, College Park, MD 20742-4015, United States
³ Department of Mathematics, Temple University, Wachman Hall, 1805 N Broad St, Philadelphia, PA 19122, United States

Geometry & topology, Tome 21 (2017) no. 1, pp. 215-251.

Résumé

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.

Détail

DOI : 10.2140/gt.2017.21.215

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

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