Hyperbolic Manifolds and Kleinian Groups (Oxford Mathematical Monographs) 1st Edition by Katsuhiko Matsuzaki (PDF)

Description

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 produced important work which helped make Kleinian groups an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought about a revolution in the field with his profound investigation of hyperbolic manifolds, and Sullivan developed an important complex dynamical approach. This book provides the fundamental results and key theorems necessary for access to the frontiers of the theory from a modern viewpoint.

User’s Reviews

Editorial Reviews: Review “The subject of this monograph is the modern theory of Kleinian groups as developed by Ahlfors, Bers, Thurston and their students. It prepares the reader for the current work on the subject.”–Mathematical Reviews About the Author Katsuhiko Matsuzaki is at Ochanomizu University. Masahiko Taniguchi is at Kyoto University.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a very well written book, it covers everything you would like to know from the scratch (in dimension three) about hyperbolic 3 manifolds and Kleinian groups. It doesn’t get pedantic or too technical like most of the other publications about the same subject. The writers don’t forget to state differences between dimensions 2 and 3 while motivating you to keep reading to learn one of the most amazing subjects of mathematics.

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