Modern Birkhäuser Classics

Hyperbolic Manifolds and Discrete Groups

Authors: Kapovich, Michael

  • Includes beautiful illustrations, a rich set of examples of key concepts, and numerous exercises
  • Contains an extensive bibliography and index that are complemented by a glossary of terms
  • Presents the first complete proof of the generic case of Thurston’s hyperbolization theorem
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eBook $79.99
price for USA (gross)
  • ISBN 978-0-8176-4913-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.00
price for USA
  • ISBN 978-0-8176-4912-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on Thurston’s hyperbolization theorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to the hyperbolization theorem as well as rich discussions on related topics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups.

Featuring beautiful illustrations, a rich set of examples, numerous exercises, and an extensive bibliography and index, Hyperbolic Manifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference.

The book is very clearly written and fairly self-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments.

---Mathematical Reviews

Beyond the hyperbolization theorem, this is an important book which had to be written; some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolization theorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research.

---Zentralbatt MATH

This book can act as source material for a postgraduate course and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated.

---ASLIB Book Guide

Reviews

From the reviews:

"This book can act as source material for a postgraduate course and as a reference text on the topic as the references are full and extensive . . . The text is self-contained and very well illustrated."

Aslib Book Guide

"The book is very clearly written and fairly self-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments."

Mathematical Reviews

"We recommend the excellent introduction of the present book for the history of the various contributions, and also for a sketch of the proof itself. . . . This is an important book which had to be written . . . the book contains a lot of material which will be useful for various other directions of research."

Zentralblatt Math

“Hyperbolic Manifolds and Discrete Groups is an essential text for anyone working in the topology and geometry of 3-manifolds. It is largely self-contained in that it defines all the needed concepts and machinery and often provides proofs of facts that can be found elsewhere in the literature. This book is most valuable for compiling all the needed concepts in one place. This collection is breath-taking in scope … . Kapovich’s book is an excellent, substantial exposition of the varied aspects of the mathematics present.” (Scott Taylor, The Mathematical Association of America, January, 2011)


Table of contents (20 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-0-8176-4913-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.00
price for USA
  • ISBN 978-0-8176-4912-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Hyperbolic Manifolds and Discrete Groups
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4913-5
DOI
10.1007/978-0-8176-4913-5
Softcover ISBN
978-0-8176-4912-8
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XXVI, 470
Number of Illustrations and Tables
78 b/w illustrations
Additional Information
Originally published as volume 183 in the series: Progress in Mathematics
Topics