Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups.

DOI10.4171/JEMS/417zbMath1292.20047arXiv0908.0705MaRDI QIDQ388768

Leonid Potyagailo, Victor Gerasimov

Publication date: 7 January 2014

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

Full work available at URL: https://arxiv.org/abs/0908.0705

zbMATH Keywords

finitely generated groupsrelatively hyperbolic groupsactions by homeomorphismsconvergence actionsFloyd boundariesquasi-isometric maps

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Topological methods in group theory (57M07) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (23)

Controlled Floyd Separation and Non Relatively Hyperbolic Groups ⋮ Some topological characterizations of rational maps and Kleinian groups ⋮ Stability phenomena for Martin boundaries of relatively hyperbolic groups ⋮ Local limit theorems in relatively hyperbolic groups II: the non-spectrally degenerate case ⋮ Floyd maps for relatively hyperbolic groups. ⋮ Patterson-Sullivan measures and growth of relatively hyperbolic groups ⋮ Glueing spaces without identifying points ⋮ Counting conjugacy classes in groups with contracting elements ⋮ The Hausdorff dimension of the harmonic measure for relatively hyperbolic groups ⋮ Relatively dominated representations from eigenvalue gaps and limit maps ⋮ Maps between relatively hyperbolic spaces and between their boundaries ⋮ Martin boundary covers Floyd boundary ⋮ Cannon-Thurston fibers for iwip automorphisms of FN ⋮ Boundaries of Dehn fillings ⋮ Entropy and drift for word metrics on relatively hyperbolic groups ⋮ Generic free subgroups and statistical hyperbolicity ⋮ Conical limit points and the Cannon-Thurston map ⋮ Thick groups have trivial Floyd boundary ⋮ Entropy and drift for Gibbs measures on geometrically finite manifolds ⋮ Genericity of contracting elements in groups ⋮ The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups ⋮ Hausdorff dimension of boundaries of relatively hyperbolic groups ⋮ Non-finitely generated relatively hyperbolic groups and Floyd quasiconvexity

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