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Hyperbolic Manifolds and Discrete Groups

Hyperbolic Manifolds and Discrete Groups
Catalogue Information
Field name Details
Dewey Class 514
Title Hyperbolic Manifolds and Discrete Groups (EB) / by Michael Kapovich.
Author Kapovich, Michael
Other name(s) SpringerLink (Online service)
Publication Boston : Birkhäuser , 2010.
Physical Details XXVII, 467 pages, 78 illus. : online resource.
Series Modern Birkhäuser classics
ISBN 9780817649135
Summary Note 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 Thurstonâs hyperbolization theorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to the hyperbolization theorem as well as rich discussions on related topics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich set of examples, numerous exercises, and an extensive bibliography and index, Hyperbolic Manifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairly self-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem, this is an important book which had to be written; some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolization theorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. ---Zentralbatt MATH This book can act as source material for a postgraduate course and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide:
Contents note Preface -- Three-dimensional Topology -- Thurston Norm.-Geometry of the Hyperbolic Space -- Kleinian Groups -- Teichmüller 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
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