Results 1 - 10 of 148

The classification of Kleinian surface groups II: The Ending Lamination Conjecture

by Jeffrey F. Brock, Richard D. Canary, Yair N. Minsky , 2004
"... Thurston’s Ending Lamination Conjecture states that a hyperbolic 3-manifold with finitely generated fundamental group is uniquely determined by its topological type and its end invariants. In this paper we prove this conjecture for Kleinian surface groups. The main ingredient is the establishment o ..."
Abstract - Cited by 108 (21 self) - Add to MetaCart
Thurston’s Ending Lamination Conjecture states that a hyperbolic 3-manifold with finitely generated fundamental group is uniquely determined by its topological type and its end invariants. In this paper we prove this conjecture for Kleinian surface groups. The main ingredient is the establishment of a uniformly bilipschitz model for a Kleinian surface group. The first half of the proof appeared in [47], and a subsequent paper [15] will establish the Ending Lamination Conjecture in general.
(Show Context)

Hyperbolic structures on 3-manifolds, I: Deformation of acylindrical manifolds

by William P. Thurston - Annals of Math , 1986
"... Abstract. This is an eprint approximation to [Thu86], which is the definitive form of this paper. This eprint is provided for convenience only; the theorem numbering of this version is different, and not all corrections are present, so any reference or quotation should refer to the published form. P ..."
Abstract - Cited by 91 (1 self) - Add to MetaCart
Abstract. This is an eprint approximation to [Thu86], which is the definitive form of this paper. This eprint is provided for convenience only; the theorem numbering of this version is different, and not all corrections are present, so any reference or quotation should refer to the published form. Parts II and III ( [Thua] and [Thub]) of this series, although accepted for publication, for many years have only existed in preprint form; they will also be made available as eprints. This is the first in a series of papers dealing with the conjecture that all compact 3-manifolds admit canonical decompositions into geometric pieces. This conjecture will be discussed in detail in part IV. Here is an easily stated special case, in which no decomposition is necessary: Conjecture 0.1 (Indecomposable Implies Geometric). Let M 3 be a closed, prime, atoroidal 3-manifold.
(Show Context)

The classification of Kleinian surface groups I: models and bounds

by Yair N. Minsky , 2002
"... Abstract. 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 thick part of the corresponding hyperbolic manifold. This enables us to describe the topologi ..."
Abstract - Cited by 86 (4 self) - Add to MetaCart
Abstract. 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 thick part of the corresponding hyperbolic manifold. This enables us to describe the topological structure of the thick part, and to give a-priori geometric bounds. Contents
(Show Context)

Group invariant Peano curves

by James W Cannon, William P Thurston , 1987
"... Our main theorem is that, if M is a closed hyperbolic 3–manifold which fibres over the circle with hyperbolic fibre S and pseudo-Anosov monodromy, then the lift of the inclusion of S in M to universal covers extends to a continuous map of B2 to B3, where Bn D Hn n 1 [ S1. The restriction to S 1 1 ma ..."
Abstract - Cited by 57 (2 self) - Add to MetaCart
Our main theorem is that, if M is a closed hyperbolic 3–manifold which fibres over the circle with hyperbolic fibre S and pseudo-Anosov monodromy, then the lift of the inclusion of S in M to universal covers extends to a continuous map of B2 to B3, where Bn D Hn n 1 [ S1. The restriction to S 1 1 maps onto S 2 1 and gives an example of an equivariant S 2 –filling Peano curve. After proving the main theorem, we discuss the case of the figure-eight knot complement, which provides evidence for the conjecture that the theorem extends to the case when S is a once-punctured hyperbolic surface. 20F65; 57M50, 57M60, 57N05, 57N60 1
(Show Context)

The classification of punctured-torus groups

by Yair N. Minsky - ANNALS OF MATH , 1999
"... Thurston’s ending lamination conjecture proposes that a finitely generated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends. We present a proof of this conjecture for punctured-torus grou ..."
Abstract - Cited by 50 (5 self) - Add to MetaCart
Thurston’s ending lamination conjecture proposes that a finitely generated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends. We present a proof of this conjecture for punctured-torus groups. These are free two-generator Kleinian groups with parabolic commutator, which should be thought of as representations of the fundamental group of a punctured torus. As a consequence we verify the conjectural topological description of the deformation space of punctured-torus groups (including Bers ’ conjecture that the quasi-Fuchsian groups are dense in this space) and prove a rigidity theorem: two punctured-torus groups are quasi-conformally conjugate if and only if they are topologically conjugate.
(Show Context)

Algebraic limits of Kleinian groups which rearrange the pages of a book

by James W. Anderson, Richard D. Canary - Zbl 0874.57012 MR 1411128 , 1996
"... Dedicated to Bernard Maskit on the occasion of his sixtieth birthday ..."
Abstract - Cited by 49 (14 self) - Add to MetaCart
Dedicated to Bernard Maskit on the occasion of his sixtieth birthday
(Show Context)

Iteration on Teichmüller space

by Curt Mcmullen - Invent. Math , 1994
"... this paper we use Riemann surface techniques to study the third iteration, and provide a new proof of a fundamental step in the geometrization of 3-manifolds. (An expository account appears in [Mc2].) ..."
Abstract - Cited by 45 (12 self) - Add to MetaCart
this paper we use Riemann surface techniques to study the third iteration, and provide a new proof of a fundamental step in the geometrization of 3-manifolds. (An expository account appears in [Mc2].)
(Show Context)

On the density of geometrically finite Kleinian groups

by Jeffrey F. Brock, Kenneth W. Bromberg , 2002
"... The density conjecture of Bers, Sullivan and Thurston predicts that each complete hyperbolic 3-manifold M with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We prove that the conjecture obtains for each complete hyperbolic 3-manifold with ..."
Abstract - Cited by 42 (10 self) - Add to MetaCart
The density conjecture of Bers, Sullivan and Thurston predicts that each complete hyperbolic 3-manifold M with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We prove that the conjecture obtains for each complete hyperbolic 3-manifold with no cusps and incompressible ends.

Cusps Are Dense

by Curt Mcmullen , 1994
"... We show cusps are dense in Bers' boundary for Teichmüller space. The proof rests on an estimate for the algebraic effect of a unit quasiconformal deformation supported in the thin part of a hyperbolic Riemann surface. ..."
Abstract - Cited by 40 (2 self) - Add to MetaCart
We show cusps are dense in Bers' boundary for Teichmüller space. The proof rests on an estimate for the algebraic effect of a unit quasiconformal deformation supported in the thin part of a hyperbolic Riemann surface.

Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion

by Alexander Fel'shtyn , 1996
"... ..."
Abstract - Cited by 39 (6 self) - Add to MetaCart
Abstract not found