Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics)

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9780387331973: Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics)

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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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 book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow’s rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincare«s fundamental polyhedron theorem.

The exposition if at the level of a second year graduate student with particular emphasis placed on readability and completeness of argument. After reading this book, the reader will have the necessary background to study the current research on hyperbolic manifolds.

The second edition is a thorough revision of the first edition that embodies hundreds of changes, corrections, and additions, including over sixty new lemmas, theorems, and corollaries. The new main results are Schl\¬afli’s differential formula and the $n$-dimensional Gauss-Bonnet theorem.

John G. Ratcliffe is a Professor of Mathematics at Vanderbilt University.

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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)

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Book Description Springer-Verlag New York Inc., United States, 2006. Hardback. Book Condition: New. 2nd ed. 2006. Language: English . Brand New Book. 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. Bookseller Inventory # AAU9780387331973

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Book Description Springer-Verlag New York Inc., United States, 2006. Hardback. Book Condition: New. 2nd ed. 2006. Language: English . Brand New Book. 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. Bookseller Inventory # AAU9780387331973

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Book Description Springer-Verlag New York Inc., 2006. Book Condition: New. 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. This book has been heavily class-tested and each chapter contains exercises and a section of historical remarks. Series: Graduate Texts in Mathematics. Num Pages: 794 pages, biography. BIC Classification: PBM; PBP. Category: (P) Professional & Vocational. Dimension: 237 x 167 x 47. Weight in Grams: 1252. . 2006. 2nd. Hardcover. . . . . . Bookseller Inventory # V9780387331973

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Book Description Springer-Verlag New York Inc. Hardback. Book Condition: new. BRAND NEW, Foundations of Hyperbolic Manifolds (2nd ed. 2006), John Ratcliffe, 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. Bookseller Inventory # B9780387331973

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Book Description Springer-Verlag New York Inc. Book Condition: New. 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. This book has been heavily class-tested and each chapter contains exercises and a section of historical remarks. Series: Graduate Texts in Mathematics. Num Pages: 794 pages, biography. BIC Classification: PBM; PBP. Category: (P) Professional & Vocational. Dimension: 237 x 167 x 47. Weight in Grams: 1252. . 2006. 2nd. Hardcover. . . . . Books ship from the US and Ireland. Bookseller Inventory # V9780387331973

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