Hyperbolic Manifolds and Discrete Groups

• Main Author: Kapovich, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston, 2010.
• Series: Modern Birkhäuser Classics
• Subjects: Mathematics.; Group theory.; Geometry.; Topology.; Manifolds (Mathematics).; Complex manifolds.; Group Theory and Generalizations.; Manifolds and Cell Complexes (incl. Diff.Topology).

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’s hyperbolization theorem, one of the central results of 3-dimensio...

Table of Contents:

• Three-Dimensional Topology
• Thurston Norm
• Geometry of Hyperbolic Space
• Kleinian Groups
• Teichmüller Theory of Riemann Surfaces
• to Orbifold Theory
• Complex Projective Structures
• Sociology of Kleinian Groups
• Ultralimits of Metric Spaces
• 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.