Zimmer's conjecture: subexponential growth, measure rigidity, and strong property (T)

DOI10.4007/annals.2022.196.3.1OpenAlexW2520471426WikidataQ122877670 ScholiaQ122877670MaRDI QIDQ2092825

Sebastian Hurtado, David Fisher, Aaron W. Brown

Publication date: 3 November 2022

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.04995

zbMATH Keywords

Lyapunov exponentsactions of latticesmeasure rigidityproperty (T)lattices in semisimple Lie groupsZimmer programactions of abelian groupsRatner theory

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) General theory of group and pseudogroup actions (22F05)

Related Items (8)

Projective and conformal closed manifolds with a higher-rank lattice action ⋮ Smooth ergodic theory of \(\mathbb{Z}^d \)-actions ⋮ Global rigidity of higher rank lattice actions with dominated splitting ⋮ Asymptotic representations of Hamiltonian diffeomorphisms and quantization ⋮ Symmetries of flat manifolds, Jordan property and the general Zimmer program ⋮ Examples of diffeomorphism group cocycles with no periodic approximation ⋮ Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds ⋮ A local characterization of Kazhdan projections and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Towards strong Banach property (T) for \(\mathrm{SL}(3,\mathbb R)\)
• Global rigidity of higher rank abelian Anosov algebraic actions
• Smooth factors of projective actions of higher-rank lattices and rigidity
• Distortion elements in group actions on surfaces
• A reinforcement of property (T)
• Volume preserving actions of lattices in semisimple groups on compact manifolds
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Large group actions on manifolds
• Strong rigidity for ergodic actions of semisimple Lie groups
• Spectrum, entropy and geometric structures for smooth actions of Kazhdan groups
• Real-analytic actions of lattices
• Lattice actions on the circle
• Invariant measures and orbit closures for unipotent actions on homogeneous spaces
• Limit distributions of polynomial trajectories on homogeneous spaces
• A proof of the Hilbert-Smith conjecture for actions by Lipschitz maps
• Growth of maps, distortion in groups and symplectic geometry
• Continuous bounded cohomology and applications to rigidity theory
• Global smooth and topological rigidity of hyperbolic lattice actions
• Nonergodic actions, cocycles and superrigidity
• A structure theorem for actions of semisimple Lie groups
• Transformation groups in differential geometry.
• Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds
• The Burnside problem for \(\text{Diff}_{\omega}(\mathbb{S}^2)\)
• A local characterization of Kazhdan projections and applications
• On discrete subgroups of Lie groups. I, II
• On the smoothness of isometries
• Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I
• Strong rigidity of Q-rank 1 lattices
• Almost isometric actions, property (T), and local rigidity
• Actions of arithmetic groups on homology spheres and acyclic homology manifolds
• The group of isometries of a Riemannian manifold
• Groups acting on manifolds: around the Zimmer program
• Arithmetic groups acting on compact manifolds
• Existence and regularity of isometries
• On Hölder continuous Riemannian and Finsler metrics
• Strong property (T) for higher-rank simple Lie groups: Figure 1.
• [https://portal.mardi4nfdi.de/wiki/Publication:4288848 Sur les groupes engendr�s par des diff�omorphismes proches de l'identit�]
• Arithmetic Groups of Higher ℚ-Rank Cannot Act on 1-Manifolds
• Global rigidity of higher rank Anosov actions on tori and nilmanifolds
• C¹ actions on manifolds by lattices in Lie groups
• Strong Banach property (T) for simple algebraic groups of higher rank
• Lectures on Lyapunov Exponents
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)
• Lie groups beyond an introduction

This page was built for publication: Zimmer's conjecture: subexponential growth, measure rigidity, and strong property (T)