Kapovich Hyperbolic Manifolds and Discrete Groups

1. Auflage 2009
ISBN: 978-0-8176-4913-5
Verlag: Birkhäuser Basel
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 470 Seiten

Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on the 'Big Monster,' i.e., on Thurston's hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology. The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.

Autoren/Hrsg.

Kapovich, Michael

Inhaltsverzeichnis

1;Preface;7
2;Contents;22
3;1. Three-Dimensional Topology;27
4;2. Thurston Norm;48
5;3. Geometry of Hyperbolic Space;56
6;4. Kleinian Groups;82
7;5. Teichmüller Theory of Riemann Surfaces;144
8;6. Introduction of Orbifold Theory;159
9;7. Complex Projective Structures;184
10;8. Sociology of Kleinian Groups;191
11;9. Ultralimits of Metric Spaces;241
12;10. Introduction to Group Actions on Treens;248
13;11. Laminations, Foliations, and Trees;263
14;12. Rips Theory;299
15;13. Brooks' Theorem and Circle Packings;353
16;14. Pleated Surfaces and Ends of Hyperbolic Manifolds;371
17;15. Outline of the Proof of the Hyperbolization Theorem;389
18;16. Reduction of the Bounded Image Theorem;397
19;17. The Bounded Image Theorem;402
20;18. Hyperbolization of Fibrations;415
21;19. The Orbifold Trick;420
22;20. Beyond the Hyperbolization Theorem;434
23;References;449
24;Index;477