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.

Reviews

From the reviews:"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"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"We recommend the excellent introduction of the present book for the history of the various contributions, and also for a sketch of the proof itself. . . . This is an important book which had to be written . . . the book contains a lot of material which will be useful for various other directions of research."—Zentralblatt Math“Hyperbolic Manifolds and Discrete Groups is an essential text for anyone working in the topology and geometry of 3-manifolds. It is largely self-contained in that it defines all the needed concepts and machinery and often provides proofs of facts that can be found elsewhere in the literature. This book is most valuable for compiling all the needed concepts in one place. This collection is breath-taking in scope … . Kapovich’s book is an excellent, substantial exposition of the varied aspects of the mathematics present.” (Scott Taylor, The Mathematical Association of America, January, 2011)