Foundations of Hyperbolic Manifolds

  • John G. Ratcliffe

Part of the Graduate Texts in Mathematics book series (GTM, volume 149)

Table of contents

  1. Front Matter
    Pages i-xi
  2. John G. Ratcliffe
    Pages 1-35
  3. John G. Ratcliffe
    Pages 36-55
  4. John G. Ratcliffe
    Pages 56-104
  5. John G. Ratcliffe
    Pages 105-147
  6. John G. Ratcliffe
    Pages 148-191
  7. John G. Ratcliffe
    Pages 192-262
  8. John G. Ratcliffe
    Pages 263-329
  9. John G. Ratcliffe
    Pages 330-370
  10. John G. Ratcliffe
    Pages 371-430
  11. John G. Ratcliffe
    Pages 431-502
  12. John G. Ratcliffe
    Pages 503-572
  13. John G. Ratcliffe
    Pages 573-651
  14. John G. Ratcliffe
    Pages 652-714
  15. Back Matter
    Pages 715-750

About this book


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. Particular emphasis has been placed on readability and completeness of ar­ gument. The treatment of the material is for the most part elementary and self-contained. 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, consisting of Chap­ ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de­ voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in­ tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.


Grad Isometrie algebra development geometry hyperbolic geometry hyperbolic manifolds knowledge manifold topology university

Authors and affiliations

  • John G. Ratcliffe
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94348-0
  • Online ISBN 978-1-4757-4013-4
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site