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Foundations of Hyperbolic Manifolds : Graduate Texts in Mathematics - John Ratcliffe

Foundations of Hyperbolic Manifolds

By: John Ratcliffe

Hardcover | 23 August 2006 | Edition Number 2

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This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. The reader is assumed to have a basic knowledge of algebra and topology at the first year graduate level of an American university. The book is divided into three parts. 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.

The second edition contains hundreds of changes and corrections, and new additions include: A more thorough discussion of polytopes; Discussion of Simplex Reflection groups has been expanded to give a complete classification of the Gram matrices of spherical, Euclidean and hyperbolic n-simplices; A new section on the volume of a simplex, in which a derivation of Schlafli's differential formula is presented; A new section with a proof of the n-dimensional Gauss-Bonnet theorem.

The exercises have been thoroughly reworked, pruned, and upgraded, and over 100 new exercises have been added. The author has also prepared a solutions manual which is available to professors who choose to adopt this text for their course.

Industry 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)

You Can Find This Book In

Non-FictionMathematicsGeometryNon-Euclidean GeometryTopologyAlgebraic Geometry

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