Overview

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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9781441922021

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The author provides a book that will serve both as a reference to experts in the area for many years to come, and potentially as a textbook to introduce this area to the more sophisticated student!This book has a tremendous amount of depth. In addition to the careful and complete exposition, each chapter ends with a fascinating section containing historical notes, putting many of the ideas into context. This volume will play an important role in the continuing development of this fascinating field. - Colin Adams, Mathematical Reviews A detailed and extensive study of geometric manifolds, esp. of hyperbolic ones, is preceded by an expose of foundations of non-Euclidean spaces, of their models and of related groups of transformations. - A. Szybiak, Zentralblatt !This book is an excellent overview of a particular branch of non-Euclidean geometry called hyperbolic geometry. There are good exercises in the book, and the author gives a detailed history of the subjects after the end of each chapter. - Lee Carlson, reader review from Amazon.com

"From the reviews of the second edition: ""Designed to be useful as both textbook and a reference, this book renders a real service to the mathematical community by putting together the tools and prerequisites needed to enter the territory of Thurston’s formidable theory of hyperbolic 3-mainfolds … . Every chapter is followed by historical notes, with attributions to the relevant literature, both of the originators of the idea present in the chapter and of modern presentation thereof. The bibliography contains 463 entries."" (Victor V. Pambuccian, Zentralblatt MATH, Vol. 1106 (8), 2007)"

The author provides a book that will serve both as a reference to experts in the area for many years to come, and potentially as a textbook to introduce this area to the more sophisticated student!This book has a tremendous amount of depth. In addition to the careful and complete exposition, each chapter ends with a fascinating section containing historical notes, putting many of the ideas into context. This volume will play an important role in the continuing development of this fascinating field. - Colin Adams, Mathematical Reviews A detailed and extensive study of geometric manifolds, esp. of hyperbolic ones, is preceded by an expose of foundations of non-Euclidean spaces, of their models and of related groups of transformations. - A. Szybiak, Zentralblatt !This book is an excellent overview of a particular branch of non-Euclidean geometry called hyperbolic geometry. There are good exercises in the book, and the author gives a detailed history of the subjects after the end of each chapter. - Lee Carlson, reader review from Amazon.com

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