Anosov representations and proper actions

Guéritaud, François¹ ; Guichard, Olivier² ; Kassel, Fanny³ ; Wienhard, Anna⁴

¹ CNRS and Laboratoire Paul Painlevé, Université Lille 1, 59655 Villeneuve d’Ascq Cedex, France
² IRMA, Université de Strasbourg, 7 rue Descartes, 67000 Strasbourg, France
³ CNRS and Laboratoire Alexander Grothendieck, Institut des Hautes Études Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, France
⁴ Mathematisches Institut, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany

Geometry & topology, Tome 21 (2017) no. 1, pp. 485-584.

Résumé

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.

Détail

DOI : 10.2140/gt.2017.21.485

Keywords: Anosov representations, properly discontinuous actions, discrete subgroups of Lie groups, representations of hyperbolic groups, boundary maps, Cartan projection

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