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Amalgam Anosov representations

Richard D Canary, Michelle Lee and Matthew Stover

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

Geometry & Topology 21 (2017) 215–251

Let Γ 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 Γ into G and prove that they form a domain of discontinuity for the action of Out(Γ). 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 Γ is Anosov, with respect to a fixed pair of opposite parabolic subgroups, then ρ is amalgam Anosov.

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character variety, Anosov representation, hyperbolic groups
Mathematical Subject Classification 2010
Primary: 20H10, 22E40, 57M50
Received: 9 November 2014
Revised: 17 December 2015
Accepted: 24 February 2016
Published: 10 February 2017
Proposed: David Gabai
Seconded: Jean-Pierre Otal, Martin Bridson
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
Matthew Stover