附註:Includes bibliographical references.
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.
摘要:Collection of papers summarising the state of the art. Ideal for graduate students or established researchers.
