CAT(-1)-spaces, divergence groups and their commensurators

DOI10.1090/S0894-0347-96-00196-8zbMath0847.22004OpenAlexW1513006141MaRDI QIDQ4874231

Shahar Mozes, Marc Burger

Publication date: 6 October 1996

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0894-0347-96-00196-8

zbMATH Keywords

local fieldsCayley graphLie groupsergodic theorylocally compact second countable grouplocally finite treediscrete groupssuperrigiditymanifolds of negative curvaturecommensurability group

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) Discrete subgroups of Lie groups (22E40) Groups acting on trees (20E08)

Related Items (41)

Factor and normal subgroup theorems for lattices in products of groups ⋮ NATURAL MAPS FOR MEASURABLE COCYCLES OF COMPACT HYPERBOLIC MANIFOLDS ⋮ On the first \(L^p\)-cohomology of discrete groups. ⋮ Multiplicative constants and maximal measurable cocycles in bounded cohomology ⋮ Bounded cohomology and totally real subspaces in complex hyperbolic geometry ⋮ Bounded differential forms, generalized Milnor-Wood inequality and an application to deformation rigidity ⋮ Fixed points and amenability in non-positive curvature ⋮ Superrigidity for homomorphisms into isometry groups of \(\text{CAT}(-1)\) spaces ⋮ Integrable measure equivalence and rigidity of hyperbolic lattices ⋮ Trees, contraction groups, and Moufang sets. ⋮ Constructing irreducible representations of discrete groups ⋮ Patterson-Sullivan measures and growth of relatively hyperbolic groups ⋮ Approximate rigidity of the marked length spectrum ⋮ Totally disconnected locally compact groups locally of finite rank ⋮ The Hopf-Tsuji-Sullivan dichotomy in higher rank and applications to Anosov subgroups ⋮ Measurable rigidity for Kleinian groups ⋮ A normal subgroup theorem for commensurators of lattices ⋮ Volume invariant and maximal representations of discrete subgroups of Lie groups ⋮ CHABAUTY LIMITS OF ALGEBRAIC GROUPS ACTING ON TREES THE QUASI-SPLIT CASE ⋮ Asymptotic Schur orthogonality in hyperbolic groups with application to monotony ⋮ Equivariant maps for measurable cocycles with values into higher rank Lie groups ⋮ Applications harmoniques entre graphes finis et un théorème de superrigidité. (Harmonic maps between finite graphs and a theorem of superrigidity.) ⋮ A theorem à la Fatou for the square root of Poisson kernel in \(\delta\)-hyperbolic spaces and decay of matrix coefficients of boundary representations ⋮ Effective mixing and counting in Bruhat–Tits trees ⋮ Coding geodesic flow on a tree ⋮ Torsion in boundary coinvariants and \(K\)-theory for affine buildings ⋮ Rank-one isometries of buildings and quasi-morphisms of Kac-Moody groups. ⋮ Lattices in product of trees ⋮ Limiting distribution of geodesics in a geometrically finite quotients of regular trees ⋮ Group actions and Helly's theorem ⋮ Homological and Bloch invariants for \(\mathbb Q\)-rank one spaces and flag structures ⋮ Simplicity and superrigidity of twin building lattices. ⋮ Coxeter-Davis lattices and commensurators ⋮ Rigidity at infinity for lattices in rank-one Lie groups ⋮ Continued fraction algorithm for Sturmian colorings of trees ⋮ (Non)-escape of mass and equidistribution for horospherical actions on trees ⋮ Isometry groups of non-positively curved spaces: structure theory ⋮ Hausdorff dimension of boundaries of relatively hyperbolic groups ⋮ A Matsumoto-Mostow result for Zimmer's cocycles of hyperbolic lattices ⋮ Group-theoretic compactification of Bruhat–Tits buildings ⋮ Some spherical functions on hyperbolic groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Covering theory for graphs of groups
• Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
• Manifolds of nonpositive curvature
• Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
• The limit set of a Fuchsian group
• Amenable ergodic group actions and an application to Poisson boundaries of random walks
• Patterson-Sullivan measures on the boundary of a hyperbolic space in the sense of Gromov
• Density of the commensurability groups of uniform tree lattices
• Some results on the geometry of convex hulls in manifolds of pinched negative curvature
• Polygonal complexes and combinatorial group theory
• Superrigidity for the commensurability group of tree lattices
• Algebraic and abstract simple groups
• A Poisson formula for semi-simple Lie groups
• Rationality properties of linear algebraic groups. II
• Curvature of Leaves in Amenable Foliations
• Uniform Tree Lattices
• Une Dichotomie de Hopf Pour les Flots Geodesiques Associes Aux Groupes Discrets D'Isometries Des Arbres
• Rigidity of Group Actions on Locally Finite Trees
• Reduction of cocycles with hyperbolic targets
• Ergodic theory and the geodesic flow on surfaces of constant negative curvature

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