Geometry & Topology

Anosov representations and proper actions

François Guéritaud, Olivier Guichard, Fanny Kassel, and Anna Wienhard

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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.

Article information

Geom. Topol., Volume 21, Number 1 (2017), 485-584.

Received: 8 June 2015
Revised: 12 January 2016
Accepted: 17 January 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 57S30: Discontinuous groups of transformations 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx] 22F30: Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40}

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


Guéritaud, François; Guichard, Olivier; Kassel, Fanny; Wienhard, Anna. Anosov representations and proper actions. Geom. Topol. 21 (2017), no. 1, 485--584. doi:10.2140/gt.2017.21.485.

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