Boundaries, rigidity of representations, and Lyapunov exponents

Abstract

In this paper we discuss some connections between measurable dynamics and rigidity aspects of group representations and group actions. A new ergodic feature of familiar group boundaries is introduced, and is used to obtain rigidity results for group representations and to prove simplicity of Lyapunov exponents for some dynamical systems.

arXiv commentFor the Proceedings of the ICM 2014, 27 pages

References in corpus (3)

• Superrigidity, Weyl groups, and actions on the Circle
• Algebraic Representations of Ergodic Actions and Super-Rigidity
• Rigidity of group actions on homogeneous spaces, III

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• Charmenability of higher rank arithmetic groups
• Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces
• Furstenberg Maps For CAT(0) Targets Of Finite Telescopic Dimension
• Some ergodic properties of metrics on hyperbolic groups
• Central Limit Theorem for Cocycles over Hyperbolic Systems
• Marked length pattern rigidity for arithmetic manifolds