In this paper we continue our geometric study of Harvey’s Complex of Curves [12], a finite dimensional and locally infinite complex C(S) associated to a surface S, which admits an action by the… (More)

Stony Brook IMS Preprint #1997/6 May 1997 Revised version: May 1998 Abstract. Thurston’s ending lamination conjecture proposes that a finitelygenerated Kleinian group is uniquely determined (up to… (More)

Thurston’s Ending Lamination Conjecture states that a hyperbolic 3manifold N with finitely generated fundamental group is uniquely determined by its topological type and its end invariants. In this… (More)

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… (More)

Many parallels have been drawn between the geometric properties of the Teichmüller space of a Riemann surface, and those of complete, negatively curved spaces (see for example [B, K2, W]). This paper… (More)

We study the Teichmüller metric on the Teichmüller 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… (More)

This note introduces and studies an open set of PSL2(C) characters of a nonabelian free group, on which the action of the outer automorphism group is properly discontinuous, and which is strictly… (More)

Contents 1. A missing line in the dictionary. 1 2. Laminations: general concepts 5 3. Natural extension and its regular part. 6 4. The Type Problem and affine structure on the leaves. 11 5.… (More)

We study the large scale geometry of the mapping class group, MCG. Our main result is that for any asymptotic cone of MCG, the maximal dimension of locally compact subsets coincides with the maximal… (More)