Anosov representations and proper actions

By Franccois Gu'eritaud, Olivier Y Guichard, Fanny Kassel, Anna Wienhard. 2015

209 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9e319739ab819cc0006e266548e2431c96cad0cb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. J. Porti
2. Anna Wienhard
3. Michael Kapovich
4. B. Leeb
5. Minju M. Lee
6. H. Oh
7. Andr'es Sambarino
8. Rafael Potrie

In Mathematical Physics

1. Anna Wienhard
2. Michael Kapovich
3. B. Leeb
4. Minju M. Lee
5. J. Porti
6. Andr'es Sambarino
7. H. Oh
8. Rafael Potrie

Citations in the corpus

• Conformality for a robust class of non-conformal attractors (2019, unknown): “[20] and in particular Bochi-Potrie-S.”
• Anosov subgroups: dynamical and geometric characterizations (2017, background): “(vi) Other characterizations of Anosov subgroups can be found in [GGKW].”
• A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings (2014, methodology): “In August 2014, the third author was present at a conference talk by Kassel where she announced some of the results which became available in February 2015 in the first version of the preprint [GGKW].”
• Anosov representations and dominated splittings (2016, methodology): “e and dominated splitting of linear cocycles. This allows us to obtain equivalent characterizations for Anosov representations and to recover recent results due to Gueritaud{Guichard{Kassel{Wienhard [GGKW] and Kapovich{ Leeb{Porti [KLP 2] by dierent methods. We also give characterizations in terms o”
• Convex cocompactness in pseudo-Riemannian hyperbolic spaces (2017, background): “[11,12,29,35] to just name a few) and now play a crucial role in higher Teichmüller theory (see e.”
• Anosov groups: local mixing, counting and equidistribution (2020, unknown): “[19] O. Guichard and A. Wienhard.”
• Invariant Measures for Horospherical Actions and Anosov Groups (2020, result): “See [16], [15] and [19] for equivalent characterizations of Anosov subgroups.”