On Livšic's theorem, superrigidity, and Anosov actions of semisimple Lie groups

DOI10.1215/S0012-7094-97-08801-3zbMath0879.22004arXivdg-ga/9606009OpenAlexW1937189586MaRDI QIDQ1363169

Ralf J. Spatzier, Edward R. Goetze

Publication date: 30 September 1997

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/dg-ga/9606009

zbMATH Keywords

semisimple Lie groupsAnosov actions

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Discrete subgroups of Lie groups (22E40) Dynamical systems with hyperbolic behavior (37D99)

Related Items (6)

Livšic theorem for matrix cocycles ⋮ Livšic theorem for matrix cocycles over nonuniformly hyperbolic systems ⋮ Equilibrium measures for certain isometric extensions of Anosov systems ⋮ Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems ⋮ Cohomology of fiber bunched cocycles over hyperbolic systems ⋮ Carnot metrics, dynamics and local rigidity

Cites Work

• On the algebraic hull of an automorphism group of a principal bundle
• Rigidity for Anosov actions of higher rank lattices
• Local rigidity for certain groups of toral automorphisms
• Actions of superrigid non-Kazhdan lattices on compact manifolds
• Connection preserving actions of connected and discrete Lie groups
• Connection preserving actions of lattices in \(SL_ n\mathbb{R}{}\)
• Topological deformation rigidity of higher rank lattice actions
• Cocycle superrigidity and rigidity for lattice actions on tori
• Global rigidity results for lattice actions on tori and new examples of volume-preserving actions
• Smooth classification of Cartan actions of higher rank semisimple Lie groups and their lattices
• Ergodicity of Anosov actions
• Infinitesimal Rigidity for the Action of SL(n, ℤ) on  n
• Tangential flatness and global rigidity of higher rank lattice actions
• Invariant manifolds
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