A small simplification in hyperbolic groups

DOI10.5802/afst.778zbMath0803.53026OpenAlexW2026660074MaRDI QIDQ1332129

Christophe Champetier

Publication date: 18 December 1994

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_1994_6_3_2_161_0

zbMATH Keywords

geodesic flowhyperbolic groupnegatively curved manifoldsgeneral metric spacessmall cancellation property

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Fundamental group, presentations, free differential calculus (57M05)

Related Items (34)

Morse quasiflats. I ⋮ Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces ⋮ Random groups, random graphs and eigenvalues of \(p\)-Laplacians ⋮ SOME SMALL CANCELLATION PROPERTIES OF RANDOM GROUPS ⋮ An introduction to pressure metrics for higher Teichmüller spaces ⋮ Flows and joins of metric spaces ⋮ The geometry of Euclidean surfaces with conical singularities ⋮ Some recent results on Anosov representations ⋮ Følner functions and the generic word problem for finitely generated amenable groups ⋮ Distinguished subgroups and quotients of hyperbolic groups ⋮ The subadditive ergodic theorem and generic stretching factors for free group automorphisms. ⋮ Anosov representations: domains of discontinuity and applications. ⋮ Margulis multiverse: Infinitesimal rigidity, pressure form and convexity ⋮ Generic-case complexity, decision problems in group theory, and random walks. ⋮ Anosov representations over closed subflows ⋮ Anosov subgroups: dynamical and geometric characterizations ⋮ Freiheitssatz and phase transition for the density model of random groups ⋮ GENERICITY OF FILLING ELEMENTS ⋮ The equivalence of some residual properties of word-hyperbolic groups ⋮ Complexes of groups and geometric small cancelation over graphs of groups ⋮ The pressure metric for Anosov representations ⋮ The pressure metric on the Margulis multiverse ⋮ Simple root flows for Hitchin representations ⋮ Topological mixing in 𝐶𝐴𝑇(-1)-spaces ⋮ Average-case complexity and decision problems in group theory. ⋮ Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups. ⋮ Growth gap in hyperbolic groups and amenability ⋮ Strong symbolic dynamics for geodesic flows on \(\operatorname{CAT}(-1)\) spaces and other metric Anosov flows ⋮ Noncommutative Poincaré duality for boundary actions of hyperbolic groups ⋮ New nonlinear hyperbolic groups ⋮ Asymptotic density and computability ⋮ Introduction to a small cancellation theorem ⋮ Collapsing of random quotients of hyperbolic groups with torsion. ⋮ Courbure mésoscopique et théorie de la toute petite simplification

Cites Work

• Filling Riemannian manifolds
• Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
• Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
• Three remarks on geodesic dynamics and fundamental group
• The space of finitely generated groups
• Canonical representatives and equations in hyperbolic groups
• Statistical properties of finitely presented groups
• Distinguished subgroups and quotients of hyperbolic groups
• PERIODIC FACTOR GROUPS OF HYPERBOLIC GROUPS
• ON RESIDUALING HOMOMORPHISMS AND G-SUBGROUPS OF HYPERBOLIC GROUPS
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