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Geometry of the complex of curves II: Hierarchical structure
Abstract. ((Without Abstract)).
Geometry of the complex of curves I: Hyperbolicity
The Complex of Curves on a Surface is a simplicial complex whose vertices are homotopy classes of simple closed curves, and whose simplices are sets of homotopy classes which can be realized
Quadratic differentials and foliations
This paper concerns the interplay between the complex structure of a Riemann surface and the essentially Euclidean geometry induced by a quadratic differential. One aspect of this geometry is the "
The Poisson boundary of the mapping class group
Abstract. A theory of random walks on the mapping class group and its non-elementary subgroups is developed. We prove convergence of sample paths in the Thurston compactification and show that the
The geometry of the disk complex
We give a distance estimate for the disk complex. We use the distance estimate to prove that the disk complex is Gromov hyperbolic. As another application of our techniques, we find an algorithm
Ergodicity of billiard flows and quadratic differentials
On considere un systeme billard de 2 objets de masses m 1 et m 2 . On montre que pour un ensemble dense de paires (m 1 ,m 2 ) ce systeme est ergodique
Asymptotic formulas on flat surfaces
We find asymptotics for the number of cylinders and saddle connections on flat surfaces. These results extend previous results of Veech.