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Graduate Texts in Mathematics

Foundations of Hyperbolic Manifolds

Authors: Ratcliffe, John

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  • ISBN 978-0-387-47322-2
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Hardcover $39.99
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  • ISBN 978-0-387-33197-3
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Softcover $39.99
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  • ISBN 978-1-4419-2202-1
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About this Textbook

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.

Reviews

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)


Table of contents (2 chapters)

Buy this book

eBook $29.99
$54.99 (listprice)
price for USA (gross)
valid through June 30, 2017
  • ISBN 978-0-387-47322-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $39.99
$74.95 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-0-387-33197-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $39.99
$74.95 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-1-4419-2202-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Foundations of Hyperbolic Manifolds
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
149
Copyright
2006
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-47322-2
DOI
10.1007/978-0-387-47322-2
Hardcover ISBN
978-0-387-33197-3
Softcover ISBN
978-1-4419-2202-1
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XII, 782
Topics