Hyperbolic Manifolds and Discrete Groups

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...

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Main Author: Kapovich, Michael
Corporate Author: SpringerLink (Online service)
Format: eBook
Published: Boston, MA Birkhäuser Boston 2010, 2010
Edition:1st ed. 2010
Series:Modern Birkhäuser Classics
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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