Hyperbolic Manifolds and Discrete Groups

  • Michael Kapovich

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Michael Kapovich
    Pages 1-21
  3. Michael Kapovich
    Pages 23-30
  4. Michael Kapovich
    Pages 31-56
  5. Michael Kapovich
    Pages 57-118
  6. Michael Kapovich
    Pages 119-133
  7. Michael Kapovich
    Pages 135-159
  8. Michael Kapovich
    Pages 161-167
  9. Michael Kapovich
    Pages 169-218
  10. Michael Kapovich
    Pages 219-225
  11. Michael Kapovich
    Pages 227-241
  12. Michael Kapovich
    Pages 243-278
  13. Michael Kapovich
    Pages 279-332
  14. Michael Kapovich
    Pages 333-350
  15. Michael Kapovich
    Pages 351-368
  16. Michael Kapovich
    Pages 377-381
  17. Michael Kapovich
    Pages 383-395
  18. Michael Kapovich
    Pages 397-401
  19. Michael Kapovich
    Pages 403-416
  20. Michael Kapovich
    Pages 417-431
  21. Back Matter
    Pages 433-467

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


3-dimensional topology Compactification Group theory Homeomorphism Kleinian groups Otal's proof Rips theory Thurston's hyperbolization theorem complex analysis foliation geometric structures on 3-manifolds hyperbolic geometry hyperbolic manifolds manifold topology

Authors and affiliations

  • Michael Kapovich
    • 1
  1. 1.Dept. MathematicsUniversity of California, DavisDavisU.S.A.

Bibliographic information