Uniform hyperbolicity of the curve graph via surgery sequences

DOI10.2140/agt.2014.14.3325zbMath1309.57015arXiv1302.5519OpenAlexW2077466652MaRDI QIDQ488567

Yong-Cai Geng, Sumit K. Garg

Publication date: 26 January 2015

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.5519

zbMATH Keywords

mapping class grouphyperbolicitycurve graph

Mathematics Subject Classification ID

Geometric group theory (20F65) General geometric structures on low-dimensional manifolds (57M50)

Related Items (32)

Hierarchical hyperbolicity of graphs of multicurves ⋮ Distance 4 curves on closed surfaces of arbitrary genus ⋮ Matching arc complexes: connectedness and hyperbolicity ⋮ The shadow of a Thurston geodesic to the curve graph ⋮ A universal Cannon-Thurston map and the surviving curve complex ⋮ Stable commutator length on mapping class groups ⋮ Efficient geodesics and an effective algorithm for distance in the complex of curves ⋮ Translation surfaces and the curve graph in genus two ⋮ Boundaries and automorphisms of hierarchically hyperbolic spaces ⋮ Uniform hyperbolicity of the graphs of curves ⋮ Projections in the curve complex arising from covering maps ⋮ Uniform fellow traveling between surgery paths in the sphere graph ⋮ Combinatorics of tight geodesics and stable lengths ⋮ Large-scale rigidity properties of the mapping class groups ⋮ Masur's criterion does not hold in the Thurston metric ⋮ Hierarchically hyperbolic spaces. II: Combination theorems and the distance formula ⋮ Random walks on mapping class groups ⋮ Many Haken Heegaard splittings ⋮ The genus of curve, pants and flip graphs ⋮ One-ended subgroups of mapping class groups ⋮ The Farrell-Jones conjecture for mapping class groups ⋮ Hyperbolicity of the graph of nonseparating multicurves ⋮ Effective generation of right-angled Artin groups in mapping class groups ⋮ Algorithms detecting stability and Morseness for finitely generated groups ⋮ Quasi-morphisms on surface diffeomorphism groups ⋮ Pseudo–Anosov mapping classes from pure mapping classes ⋮ Uniform hyperbolicity of the graphs of nonseparating curves via bicorn curves ⋮ Big Mapping Class Groups: An Overview ⋮ Geodesics in the mapping class group ⋮ Geometric approaches to braid groups and mapping class groups ⋮ Large-scale rank and rigidity of the Weil-Petersson metric ⋮ Hyperbolic relatively hyperbolic graphs and disk graphs

Cites Work

• Unnamed Item
• The free splitting complex of a free group. I: Hyperbolicity.
• Uniform hyperbolicity of the graphs of curves
• Geometry and rigidity of mapping class groups.
• The classification of Kleinian surface groups. II: The Ending lamination conjecture
• Hyperbolicity in Teichmüller space
• Uniform hyperbolicity of the curve graphs
• On triangulations of surfaces
• The classification of Kleinian surface groups. I: Models and bounds
• Covers and the curve complex
• The virtual cohomological dimension of the mapping class group of an orientable surface
• The classification of punctured-torus groups
• Geometry of the complex of curves. II: Hierarchical structure
• Geometry of the complex of curves. I: Hyperbolicity
• Asymptotics of Weil-Petersson geodesics. I: Ending laminations, recurrence, and flows
• 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs
• A characterization of short curves of a Teichmüller geodesic
• The hyperbolicity of the sphere complex via surgery paths
• Hyperbolicity of the complex of free factors.
• Intersection numbers and the hyperbolicity of the curve complex

This page was built for publication: Uniform hyperbolicity of the curve graph via surgery sequences