Anosov subgroups: dynamical and geometric characterizations

By Michael Kapovich, B. Leeb, J. Porti. 2017

183 citations recorded by the source corpus.

We study infinite covolume discrete subgroups of higher rank semisimple Lie groups, motivated by understanding basic properties of Anosov subgroups from various viewpoints (geometric, coarse geometric and dynamical). The class of Anosov subgroups constitutes a natural generalization of convex cocompact subgroups of rank one Lie groups to higher rank. Our main goal is to give several new equivalent characterizations for this important class of discrete subgroups. Our characterizations capture “rank one behavior” of Anosov subgroups and are direct generalizations of rank one equivalents to convex cocompactness. Along the way, we considerably simplify the original definition, avoiding the geodesic flow. We also show that the Anosov condition can be relaxed further by requiring only non-uniform unbounded expansion along the (quasi)geodesics in the group.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0fe791bba95a2bd90f374709953e351353c19ecb

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Citations in the corpus

Anosov groups: local mixing, counting and equidistribution (2020, unknown): “[24] M. Kapovich, B. Leeb, and J. Porti.”
Invariant Measures for Horospherical Actions and Anosov Groups (2020, background): “We also refer to the work of Kapovich, Leeb and Porti [19] for other equivalent characterizations of Anosov groups, as well as to excellent survey articles by Kassel and Wienhard ([20], [45]) on higher Teichmüller theory.”