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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Anosov representations and proper actions

François Guéritaud, Olivier Guichard, Fanny Kassel and Anna Wienhard

Geometry & Topology 21 (2017) 485–584
Abstract

We establish several characterizations of Anosov representations of word hyperbolic groups into real reductive Lie groups, in terms of a Cartan projection or Lyapunov projection of the Lie group. Using a properness criterion of Benoist and Kobayashi, we derive applications to proper actions on homogeneous spaces of reductive groups.

Keywords
Anosov representations, properly discontinuous actions, discrete subgroups of Lie groups, representations of hyperbolic groups, boundary maps, Cartan projection
Mathematical Subject Classification 2000
Primary: 22E40, 57S30, 37D40, 20H10, 22F30
References
Publication
Received: 8 June 2015
Revised: 12 January 2016
Accepted: 17 January 2016
Published: 10 February 2017
Proposed: Benson Farb
Seconded: Walter Neumann, Martin Bridson
Authors
François Guéritaud
CNRS and Laboratoire Paul Painlevé
Université Lille 1
59655 Villeneuve d’Ascq Cedex
France
Olivier Guichard
IRMA
Université de Strasbourg
7 rue Descartes
67000 Strasbourg
France
Fanny Kassel
CNRS and Laboratoire Alexander Grothendieck
Institut des Hautes Études Scientifiques
35 route de Chartres
91440 Bures-sur-Yvette
France
Anna Wienhard
Mathematisches Institut
Ruprecht-Karls Universität Heidelberg
Im Neuenheimer Feld 288
D-69120 Heidelberg
Germany