## About this book

### Introduction

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**

### Keywords

### Bibliographic information

- DOI https://doi.org/10.1007/978-0-8176-4913-5
- Copyright Information Birkhäuser Boston 2010
- Publisher Name Birkhäuser Boston
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-8176-4912-8
- Online ISBN 978-0-8176-4913-5
- Buy this book on publisher's site