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Kleinian groups and hyperbolic 3-manifolds : proceedings of the Warwick Workshop, September 11-14, 2001

Author: Y Komori; V Markovic; Caroline Series
Publisher: Cambridge ; New York : Cambridge University Press, 2003.
Series: London Mathematical Society lecture note series, 299.
Edition/Format:   eBook : Document : Conference publication : EnglishView all editions and formats
Database:WorldCat
Summary:
Collection of papers summarising the state of the art. Ideal for graduate students or established researchers.
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Genre/Form: Electronic books
Conference papers and proceedings
Congresses
Additional Physical Format: Print version:
Kleinian groups and hyperbolic 3-manifolds.
Cambridge ; New York : Cambridge University Press, 2003
(DLC) 2004273945
(OCoLC)52828967
Material Type: Conference publication, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Y Komori; V Markovic; Caroline Series
ISBN: 0511065647 9780511065644 9780511542817 051154281X 9780521540131 0521540135 9780511067778 0511067771
OCLC Number: 60326655
Description: 1 online resource (vii, 384 pages) : illustrations.
Contents: Cover; Series-title; Title; Copyright; Contents; Preface; Part I Hyperbolic 3-manifolds; Combinatorial and geometrical aspects of hyperbolic 3-manifolds; 1. Introduction; 1.1. Object of Study; 1.2. Kleinian surface groups; 1.3. Models and bounds; 1.4. Plan; 2. Curve complex and model manifold; 2.1. The complex of curves; 2.2. Model construction; 2.3. Geometry of the model; 3. From ending laminations to model manifold; 3.1. Background; 4. The quasiconvexity argument; 4.1. The bounded-curve projection; 4.2. Definition of Pi; 5. Quasiconvexity and projection bounds. 5.1. Relative bounds for subsurfaces5.2. Penetration in Margulis tubes; 5.3. Proof of the tube penetration theorem; 6. A priori length bounds and model map; 6.1. Proving the a priori bounds; 6.2. Constructing the Lipschitz map; 6.3. Consequences; References; Harmonic deformations of hyperbolic 3-manifolds; 1. Introduction; 2. Deformations of hyperbolic structures; 3. Infinitesimal harmonic deformations; 4. Effective Rigidity; 5. A quantitative hyperbolic Dehn surgery theorem; 6. Kleinian groups and boundary value theory; References; Cone-manifolds and the density conjecture; 1. Introduction. 1.1. Approximating the ends1.2. Realizing ends on a Bers boundary; 1.3. Candidate approximates; 1.4. Plan of the paper; 1.5. Acknowledgments; 2. Cone-deformations; 2.1. The drilling theorem; 3. Grafting short geodesics; 3.1. Graftings as cone-manifolds.; 3.2. Simultaneous grafting; 4. Drilling and asymptotic isolation of ends; 4.1. Example; 4.2. Isolation of ends; 4.3. Realizing ends in Bers compactifications; 4.4. Binding realizations; 5. Incompressible ends; References; Les géodésiques fermées d'une variété hyperbolique en tant que nœuds. Closed geodesics in a hyperbolic manifold, viewed as knots1. Introduction; 2. Les géodésiques courtes dans une variété hyperbolique homéo-morphe à S R; 3. Le cas des variétés à bord compressible; Références; Ending laminations in the Masur domain; 1. Introduction; 2. Preliminaries; 2.1. Compact cores; 2.2. Compression bodies; 2.3. Function groups; 2.4. Boundary groups; 2.5. Laminations on surfaces; 2.6. Pleated surfaces; 3. Laminations on the exterior boundary; 4. Compactness theorem; 5. Main results; References; Quasi-arcs in the limit set of a singly degenerate group with bounded geometry. 1. Introduction2. Preliminaries; 2.1. Notation; 2.2. Model manifolds; 3. Proof of theorems; 3.1. Proof of Theorem 1.3; 3.2. Proof of Theorem 1.2; 3.3. Proof of Theorem 1.1; 3.4. Uncountably many quasi-arcs; References; On hyperbolic and spherical volumes for knot and link cone-manifolds; 1. Introduction; 2. Trigonometrical identities for knots and links; 2.1. Cone-manifolds, complex distances and lengths; 2.2. Whitehead link cone-manifold; 2.3. The Borromean cone-manifold; 3. Explicit volume calculation; 3.1. The Schläfli formula; 3.2. Volume of the Whitehead link cone-manifold. 3.3. Volume of the Borromean rings cone-manifold.
Series Title: London Mathematical Society lecture note series, 299.
Responsibility: edited by Y. Komori, V. Markovic, C. Series.
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