Anosov representations and proper actions

TL;DR

This paper characterizes Anosov representations of hyperbolic groups into Lie groups using projections and applies a properness criterion to study proper actions on homogeneous spaces.

Contribution

It provides new characterizations of Anosov representations and links them to proper actions on homogeneous spaces of reductive groups.

Findings

Characterizations of Anosov representations via Cartan and Lyapunov projections

Application of properness criterion to actions on homogeneous spaces

Insights into the structure of hyperbolic group representations

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.