Hyperbolic actions of higher-rank lattices come from rank-one factors

Uri Bader; Pierre Emmanuel Caprace; Alex Furman; Alessandro Sisto

doi:10.1017/etds.2024.65

Hyperbolic actions of higher-rank lattices come from rank-one factors

Uri Bader, Pierre Emmanuel Caprace, Alex Furman, Alessandro Sisto

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Abstract

We study actions of higher rank lattices Γ < G on hyperbolic spaces, and we show that all such actions satisfying mild properties come from the rank-one factors of G. In particular, all non-elementary isometric actions on an unbounded hyperbolic space are of this type.

Original language	English
Pages (from-to)	961-988
Number of pages	28
Journal	Ergodic Theory and Dynamical Systems
Volume	45
Issue number	4
Early online date	30 Sept 2024
DOIs	https://doi.org/10.1017/etds.2024.65
Publication status	Published - Apr 2025

Keywords

Poisson boundary
discrete subgroup of semisimple Lie group
hyperbolic space
superrigidity

ASJC Scopus subject areas

Applied Mathematics
General Mathematics

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title = "Hyperbolic actions of higher-rank lattices come from rank-one factors",

abstract = "We study actions of higher rank lattices Γ < G on hyperbolic spaces, and we show that all such actions satisfying mild properties come from the rank-one factors of G. In particular, all non-elementary isometric actions on an unbounded hyperbolic space are of this type.",

keywords = "Poisson boundary, discrete subgroup of semisimple Lie group, hyperbolic space, superrigidity",

author = "Uri Bader and Caprace, {Pierre Emmanuel} and Alex Furman and Alessandro Sisto",

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AU - Sisto, Alessandro

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AB - We study actions of higher rank lattices Γ < G on hyperbolic spaces, and we show that all such actions satisfying mild properties come from the rank-one factors of G. In particular, all non-elementary isometric actions on an unbounded hyperbolic space are of this type.

KW - Poisson boundary

KW - discrete subgroup of semisimple Lie group

KW - hyperbolic space

KW - superrigidity

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DO - 10.1017/etds.2024.65

M3 - Article

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Hyperbolic actions of higher-rank lattices come from rank-one factors

Abstract

Keywords

ASJC Scopus subject areas

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