Foundations of Hyperbolic Manifolds

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Overview

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.

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Product Details

  • ISBN-13: 9780387943480
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 9/28/1994
  • Series: Graduate Texts in Mathematics
  • Edition description: Older Edition
  • Pages: 768
  • Product dimensions: 6.19 (w) x 9.31 (h) x 1.45 (d)

Table of Contents

Preface
1 Euclidean Geometry 1
2 Spherical Geometry 36
3 Hyperbolic Geometry 56
4 Inversive Geometry 105
5 Isometries of Hyperbolic Space 148
6 Geometry of Discrete Groups 192
7 Classical Discrete Groups 263
8 Geometric Manifolds 330
9 Geometric Surfaces 371
10 Hyperbolic 3-Manifolds 431
11 Hyperbolic n-Manifolds 503
12 Geometrically Finite n-Manifolds 573
13 Geometric Orbifolds 652
Bibliography 715
Index 736
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