Train tracks and the Gromov boundary of the complex of curves

2004/09/30 by Ursula Hamenstaedt, U. Hamenstaedt, Hamenstaedt, U. · 15 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DG #math.GT #msc:53H99

paper · pdf · doi:10.48550/arxiv.math/0409611

17 p, 2 figures

arxiv created 2005/02/12 · arxiv updated 2009/12/01

Abstract

We give a combinatorial proof of an unpublished result of E. Klarreich: The Gromov boundary of the complex of curves of a non-exceptional oriented surface S of finite type can naturally be identified with the space of minimal geodesic laminations on S which fill up S, equipped with a coarse Hausdorff topology.

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• The classification of Kleinian surface groups, II: The Ending Lamination Conjecture
• Path-connectivity of the set of uniquely ergodic and cobounded foliations
• Cylinder curves in finite holonomy flat metrics
• Distance in the curve graph
• Asymptotics of Weil-Petersson geodesics II: bounded geometry and unbounded entropy
• Bounded cohomology and isometry groups of hyperbolic spaces
• Bounded Pluriharmonic Functions and Holomorphic Functions on Teichmüller Space II -- Poisson integral formula --
• Sur les Automorphismes de Groupes Libres et de Groupes de Surface
• Linear progress in the complex of curves
• Limit sets of Teichm "uller geodesics with minimal non-uniquely ergodic\n vertical foliation
• On random walks on the mapping class group
• Small eigenvalues of random 3-manifolds
• Teichmueller flow and Weil-Petersson flow
• Geometric approach to Ending Lamination Conjecture
• Bernoulli measures for the Teichmueller flow

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