Foundations of Hyperbolic Manifolds

✍ Scribed by John G. Ratcliffe (auth.)

• Publisher: Springer New York
• Year: 1994
• Tongue: English
• Leaves: 760
• Series: Graduate Texts in Mathematics 149
• Category: Library

✦ Synopsis

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, Chapters 1-7, is concerned with hyperbolic geometry and discrete groups. The second part, Chapters 8-12, is devoted to the theory of hyperbolic manifolds. The third part, Chapter 13, integrates the first two parts in a development of the theory of hyperbolic orbifolds. There are over 500 exercises in this book and more than 180 illustrations.

✦ Table of Contents

Front Matter....Pages i-xi
Euclidean Geometry....Pages 1-35
Spherical Geometry....Pages 36-55
Hyperbolic Geometry....Pages 56-104
Inversive Geometry....Pages 105-147
Isometries of Hyperbolic Space....Pages 148-191
Geometry of Discrete Groups....Pages 192-262
Classical Discrete Groups....Pages 263-329
Geometric Manifolds....Pages 330-370
Geometric Surfaces....Pages 371-430
Hyperbolic 3-Manifolds....Pages 431-502
Hyperbolic n -Manifolds....Pages 503-572
Geometrically Finite n -Manifolds....Pages 573-651
Geometric Orbifolds....Pages 652-714
Back Matter....Pages 715-750

✦ Subjects

Geometry; Algebraic Geometry; Topology