A Characterization of Cocompact Hyperbolic and Finite-Volume Hyperbolic Groups in Dimension Three

DOI10.2307/2154172zbMath0761.57008OpenAlexW4255230552MaRDI QIDQ4000841

Daryl Cooper, James W. Cannon

Publication date: 26 September 1992

Full work available at URL: https://doi.org/10.2307/2154172

zbMATH Keywords

Cayley graphcocompact group of isometries of the hyperbolic 3-spacegroups of finite volumestandard hyperbolic metricword-metric

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Relations of low-dimensional topology with graph theory (57M15) Fundamental group, presentations, free differential calculus (57M05) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Quasiconformal mappings in the complex plane (30C62)

Related Items (21)

Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups ⋮ The combinatorial Riemann mapping theorem ⋮ Flows and joins of metric spaces ⋮ Large-scale conformal rigidity in dimension three ⋮ Hyperbolic convexes and quasiisometries. ⋮ Specializing cubulated relatively hyperbolic groups ⋮ Geometry and rigidity of mapping class groups. ⋮ Quasi-isometric rigidity of the class of convex-cocompact Kleinian groups ⋮ Quasi-isometric classification of graph manifold groups. ⋮ Recognizing constant curvature discrete groups in dimension 3 ⋮ Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces ⋮ Commensurability of hyperbolic manifolds with geodesic boundary ⋮ Boundaries of Dehn fillings ⋮ Relative hyperbolicity and relative quasiconvexity for countable groups. ⋮ Metric conformal structures and hyperbolic dimension ⋮ Dehn filling in relatively hyperbolic groups. ⋮ Hyperbolic groups with planar boundaries ⋮ The relative hyperbolicity and manifold structure of certain right-angled Coxeter groups ⋮ Quasi-actions on trees II: Finite depth Bass-Serre trees ⋮ The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group ⋮ Relatively dominated representations

Cites Work

• The combinatorial structure of cocompact discrete hyperbolic groups
• Group completions and limit sets of Kleinian groups
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Quasiconformal extension from dimension n to n+1
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)
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