Hyperbolic Manifolds and Discrete Groups

• Main Author: Kapovich, Michael. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston : Birkhũser Boston, 2010.
• Series: Modern Birkhũser Classics
• Subjects: Mathematics.; Group theory.; Geometry.; Topology.; Cell aggregation > Mathematics.; Group Theory and Generalizations.; Manifolds and Cell Complexes (incl. Diff.Topology).
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-4913-5

This classic book 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 Thurston<U+0019>s hyperbolization theorem, one of the central results...

Table of Contents:

• Preface
• Three-dimensional Topology
• Thurston Norm.-Geometry of the Hyperbolic Space
• Kleinian Groups
• Teichm<U+00fc>ller Theory of Riemann Surfaces
• Introduction to the Orbifold Theory
• Complex Projective Structures
• Sociology of Kleinian Groups.-Ultralimits of Metric Spaces
• Introduction to Group Actions on Trees
• Laminations, Foliations and Trees
• Rips Theory
• Brooks' Theorem and Circle Packings
• Pleated Surfaces and Ends of Hyperbolic Manifolds
• Outline of the Proof of the Hyperbolization Theorem
• Reduction to The Bounded Image Theorem
• The Bounded Image Theorem
• Hyperbolization of Fibrations
• The Orbifold Trick
• Beyond the Hyperbolization Theorem References
• Index.