Foundations of Hyperbolic Manifolds
Foundations of Hyperbolic Manifolds by John Ratcliffe is a comprehensive resource published by Springer New York on November 23, 2010. This softcover reprint of the hardcover 2nd edition from 2006 spans 782 pages and is presented in English. The book serves as both a textbook and a reference, focusing on the theoretical foundations of hyperbolic manifolds, assuming a basic knowledge of algebra and topology at the first-year graduate level.
Readers will find a structured exploration of hyperbolic geometry and discrete groups in the first part, followed by an in-depth examination of hyperbolic manifolds in the second part. The third section integrates these concepts through the development of hyperbolic orbifolds. Each chapter includes exercises to reinforce learning and a section dedicated to historical remarks, providing context to the material. A solutions manual is also available separately for those seeking additional support.
Official synopsis Publisher
This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.
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