Hyperbolic manifolds and discrete groups
著者
書誌事項
Hyperbolic manifolds and discrete groups
（Modern Birkhäuser classics）
Birkhäuser, 2009, c2001
- : pbk
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注記
Reprint. Originally published: Boston : Birkhäuser, 2001
"Reprint of the 2001 edition"
"Originally published in the Progress in mathematics series"--T.p. verso
Includes bibliographical references (p. [433]-460) and index
内容説明・目次
内容説明
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.
目次
Preface.-Three-dimensional Topology.-Thurston Norm.-Geometry of the Hyperbolic Space.-Kleinian Groups.-Teichmuller 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.
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