Authors:
- Carefully written textbook that has been heavily class-tested
- Each chapter contains exercises and a section of historical remarks
- Contains over 150 figures
- Solutions manual available separately
- Includes supplementary material: sn.pub/extras
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Graduate Texts in Mathematics (GTM, volume 149)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
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.
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)
Authors and Affiliations
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Department of Mathematics, Stevenson Center 1326, Vanderbilt University, Nashville
John G. Ratcliffe
Bibliographic Information
Book Title: Foundations of Hyperbolic Manifolds
Authors: John G. Ratcliffe
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-0-387-47322-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2006
Hardcover ISBN: 978-0-387-33197-3Published: 23 August 2006
Softcover ISBN: 978-1-4419-2202-1Published: 23 November 2010
eBook ISBN: 978-0-387-47322-2Published: 25 November 2006
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XII, 782
Topics: Geometry, Topology, Algebraic Geometry