Foundations of Hyperbolic Manifolds by John RatcliffeFoundations of Hyperbolic Manifolds by John Ratcliffe

Foundations of Hyperbolic Manifolds

byJohn Ratcliffe

Paperback | November 23, 2010

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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.
Title:Foundations of Hyperbolic ManifoldsFormat:PaperbackDimensions:795 pages, 9.25 × 6.1 × 0 inPublished:November 23, 2010Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1441922024

ISBN - 13:9781441922021

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Table of Contents

Preface.- Euclidean Geometry.- Spherical Geometry.- Hyperbolic Geometry.- Inversive Geometry.- Isometries of Hyperbolic Space.- Geometry of Discrete Groups.- Classical Discrete Groups.- Geometric Manifolds.- Geometric Surfaces.- Hyperbolic 3-Manifolds.- Hyperbolic n-Manifolds.- Geometrically Finite n-Manifolds.- Geometric Orbifolds.- Bibliography.- Index.

Editorial Reviews

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)