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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
The classification of Kleinian surface groups I : Models and bounds : preprint
We give the first part of a proof of Thurston’s Ending Lamination conjecture. In this part we show how to construct from the end invariants of a Kleinian surface group a “Lipschitz model” for the
Thurston’s Ending Lamination Conjecture states that a hyperbolic 3manifold N with nitely generated fundamental group is uniquely determined by its topological type and its end invariants. In this
The classification of punctured-torus groups.
Thurston’s ending lamination conjecture proposes that a flnitely generated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that
Extremal length estimates and product regions in Teichm
We study the Teichm\"uller metric on the Teichm\"uller space of a surface of finite type, in regions where the injectivity radius of the surface is small. The main result is that in such regions the
Bounded geometry for Kleinian groups
Abstract.We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an
Quasiconvexity in the curve complex
Let S be the boundary of a handlebody M. We prove that the set of curves in S that are boundaries of disks in M, considered as a subset of the complex of curves of S, is quasi-convex.