Volume 21, issue 1 (2017)

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Anosov representations and proper actions

François Guéritaud, Olivier Guichard, Fanny Kassel and Anna Wienhard

Geometry & Topology 21 (2017) 485–584

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.

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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
Received: 8 June 2015
Revised: 12 January 2016
Accepted: 17 January 2016
Published: 10 February 2017
Proposed: Benson Farb
Seconded: Walter Neumann, Martin Bridson
François Guéritaud
CNRS and Laboratoire Paul Painlevé
Université Lille 1
59655 Villeneuve d’Ascq Cedex
Olivier Guichard
Université de Strasbourg
7 rue Descartes
67000 Strasbourg
Fanny Kassel
CNRS and Laboratoire Alexander Grothendieck
Institut des Hautes Études Scientifiques
35 route de Chartres
91440 Bures-sur-Yvette
Anna Wienhard
Mathematisches Institut
Ruprecht-Karls Universität Heidelberg
Im Neuenheimer Feld 288
D-69120 Heidelberg