Ergodic theory, semisimple Lie groups, and foliations by manifolds of negative curvature

DOI10.1007/BF02698694zbMath0525.57022OpenAlexW2055544534WikidataQ115391869 ScholiaQ115391869MaRDI QIDQ585588

Robert J. Zimmer

Publication date: 1982

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1982__55__37_0

zbMATH Keywords

Furstenberg boundaryboundary at infinityamenable actionasymptotic geodesics in leafergodic actions of connected semi-simple Lie groups of rank greater than 1 and without compact factorsergodic measurable foliations in which the leaves are Riemannian symmetric spaces of noncompact typeleaves with variable sectional curvature bounded above by negative constantrigidity of ergodic actions of semisimple Lie groups

Mathematics Subject Classification ID

General groups of measure-preserving transformations (28D15) Foliations (differential geometric aspects) (53C12) Differential geometry of symmetric spaces (53C35) Foliations in differential topology; geometric theory (57R30) Noncompact Lie groups of transformations (57S20)

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Factor and normal subgroup theorems for lattices in products of groups ⋮ Reduction of cocycles with hyperbolic targets ⋮ A foliated metric rigidity theorem for higher rank irreducible symmetric spaces ⋮ Convex-invariant means and a pathwise central limit theorem ⋮ Problems on rigidity of group actions and cocycles ⋮ Foliations with leaves of nonpositive curvature ⋮ Some new rigidity results for stable orbit equivalence ⋮ Indecomposability of treed equivalence relations ⋮ Limit distributions of expanding translates of certain orbits on homogeneous spaces ⋮ The stretch of a foliation and geometric superrigidity ⋮ Stabilizers of ergodic actions of lattices and commensurators ⋮ Subrelations of ergodic equivalence relations ⋮ Stabilizers of actions of lattices in products of groups ⋮ Minimal actions of semisimple groups ⋮ Deformations of totally geodesic foliations and minimal surfaces in negatively curved 3-manifolds ⋮ Stabilizer rigidity in irreducible group actions ⋮ The Nevo-Zimmer intermediate factor theorem over local fields ⋮ A generalization of the intermediate factors theorem ⋮ Rigidity of group actions on homogeneous spaces. III ⋮ Minimal entropy rigidity for foliations of compact spaces ⋮ Superharmonic Functions on Foliations ⋮ Structure properties of laminar currents on \(\mathbb{P}^2\) ⋮ Rank rigidity for foliations by manifolds of nonpositive curvature ⋮ Rigidity of Furstenberg entropy for semisimple Lie group actions ⋮ Splitting of nonnegatively curved leaves in minimal sets of foliations ⋮ On the automorphism group of a compact Lorentz manifold and other geometric manifolds

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