# Foundations of Hyperbolic Manifolds

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

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

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

- DOI https://doi.org/10.1007/978-1-4757-4013-4
- 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
- About this book