Hyperbolic Manifolds and Kleinian Groups

By: Katsuhiko Matsuzaki, Masahiko Taniguchi

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Hardcover | 30 April 1998

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Hardcover
264 Pages

Dimensions(cm)
24.77 x 16.51 x 1.91

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A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers were the leading researchers of Kleinian groups and helped it to become an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought a revolution to this area with his profound investigation of hyperbolic manifolds, and at the same time complex dynamical approach was strongly developed by Sullivan. This book provides fundamental results and important theorems which are needed for access to the frontiers of the theory from a modern viewpoint.

Industry Reviews

'The presentation of the whole theory is very nice...the book reads well, and will be interesting and accessible for mathematicians from several branches of mathematics' EMS

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