Anosov representations and proper actions

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.

73 pages, 4 figures; to appear in Geometry & Topology

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• SO(p,q)-Higgs bundles and higher Teichmüller components
• Geometry of compact complex manifolds associated to generalized quasi-Fuchsian representations
• Affine Anosov representations and proper actions
• Positivity and representations of surface groups
• Rank One Hilbert Geometries
• Cubulated hyperbolic groups admit Anosov representations
• Strict contractions and exotic SO_0(d,1) quotients
• Borel and volume classes for dense representations of discrete groups
• Cataclysms for Anosov representations
• Anosov representations acting on homogeneous spaces: domains of discontinuity
• Discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank
• Geometric structures for maximal representations and pencils