Hyperbolic Manifolds and Kleinian Groups

Hardcover | January 1, 1998

byKatsuhiko Matsuzaki, Masahiko Taniguchi

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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 Mobius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry andcomplex 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 Teichmuller 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.

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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 Mobius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry andcomplex analysis. After 1960, Ahlfors and Bers...

Katsuhiko Matsuzaki is at Ochanomizu University. Masahiko Taniguchi is at Kyoto University.
Format:HardcoverDimensions:264 pages, 9.21 × 6.14 × 0.75 inPublished:January 1, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198500629

ISBN - 13:9780198500629

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Table of Contents

0. Hyperbolic surfaces and Fuchsian groups: summary1. Hyperbolic 3-manifolds2. The basis of Kleinian group theory3. Geometrically finite Kleinian groups4. Finitely generated Kleinian groups5. The sphere at infinity6. Infinite ends of hyperbolic manifolds7. Algebraic and geometric convergencesAppendixReferences

Editorial 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