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148
The classification of Kleinian surface groups II: The Ending Lamination Conjecture
, 2004
"... Thurston’s Ending Lamination Conjecture states that a hyperbolic 3manifold 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 ..."
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Cited by 108 (21 self)
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Thurston’s Ending Lamination Conjecture states that a hyperbolic 3manifold 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.
Hyperbolic structures on 3manifolds, I: Deformation of acylindrical manifolds
 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 ..."
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Cited by 91 (1 self)
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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 3manifolds 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 3manifold.
The classification of Kleinian surface groups I: models and bounds
, 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 ..."
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Cited by 86 (4 self)
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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 apriori geometric bounds. Contents
Group invariant Peano curves
, 1987
"... Our main theorem is that, if M is a closed hyperbolic 3–manifold which fibres over the circle with hyperbolic fibre S and pseudoAnosov 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 ..."
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Cited by 57 (2 self)
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Our main theorem is that, if M is a closed hyperbolic 3–manifold which fibres over the circle with hyperbolic fibre S and pseudoAnosov 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 figureeight knot complement, which provides evidence for the conjecture that the theorem extends to the case when S is a oncepunctured hyperbolic surface. 20F65; 57M50, 57M60, 57N05, 57N60 1
The classification of puncturedtorus groups
 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 puncturedtorus grou ..."
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Cited by 50 (5 self)
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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 puncturedtorus groups. These are free twogenerator 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 puncturedtorus groups (including Bers ’ conjecture that the quasiFuchsian groups are dense in this space) and prove a rigidity theorem: two puncturedtorus groups are quasiconformally conjugate if and only if they are topologically conjugate.
Algebraic limits of Kleinian groups which rearrange the pages of a book
 Zbl 0874.57012 MR 1411128
, 1996
"... Dedicated to Bernard Maskit on the occasion of his sixtieth birthday ..."
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Cited by 49 (14 self)
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Dedicated to Bernard Maskit on the occasion of his sixtieth birthday
Iteration on Teichmüller space
 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 3manifolds. (An expository account appears in [Mc2].) ..."
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Cited by 45 (12 self)
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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 3manifolds. (An expository account appears in [Mc2].)
On the density of geometrically finite Kleinian groups
, 2002
"... The density conjecture of Bers, Sullivan and Thurston predicts that each complete hyperbolic 3manifold M with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3manifolds. We prove that the conjecture obtains for each complete hyperbolic 3manifold with ..."
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Cited by 42 (10 self)
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The density conjecture of Bers, Sullivan and Thurston predicts that each complete hyperbolic 3manifold M with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3manifolds. We prove that the conjecture obtains for each complete hyperbolic 3manifold with no cusps and incompressible ends.
Cusps Are Dense
, 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. ..."
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Cited by 40 (2 self)
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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.