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The Hyperbolization Theorem for Fibered 3-Manifolds
Jean-Pierre Otal, ENS-Lyon, France
A co-publication of the AMS and Société Mathématique de France.
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SMF/AMS Texts and Monographs
2001; 126 pp; softcover
Volume: 7
ISBN-10: 0-8218-2153-9
ISBN-13: 978-0-8218-2153-4
List Price: US$45
Member Price: US$36
Order Code: SMFAMS/7
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A fundamental element of the study of 3-manifolds is Thurston's remarkable geometrization conjecture, which states that the interior of every compact 3-manifold has a canonical decomposition into pieces that have geometric structures. In most cases, these structures are complete metrics of constant negative curvature, that is to say, they are hyperbolic manifolds. The conjecture has been proved in some important cases, such as Haken manifolds and certain types of fibered manifolds. The influence of Thurston's hyperbolization theorem on the geometry and topology of 3-manifolds has been tremendous. This book presents a complete proof of the hyperbolization theorem for 3-manifolds that fiber over the circle, following the plan of Thurston's original (unpublished) proof, though the double limit theorem is dealt with in a different way.

The book is suitable for graduate students with a background in modern techniques of low-dimensional topology and will also be of interest to researchers in geometry and topology.

This is the English translation of a volume originally published in 1996 by the Société Mathématique de France.

Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.

Readership

Graduate students and research mathematicians interested in low-dimensional topology and geometry.

Reviews

From a review of the French edition:

"The book is very well written ... completely self-contained ..."

-- Mathematical Reviews

Table of Contents

  • Teichmüller spaces and Kleinian groups
  • Real trees and degenerations of hyperbolic structures
  • Geodesic laminations and real trees
  • Geodesic laminations and the Gromov topology
  • The double limit theorem
  • The hyperbolization theorem for fibered manifolds
  • Sullivan's theorem
  • Actions of surface groups on real trees
  • Two examples of hyperbolic manifolds that fiber over the circle
  • Geodesic laminations
  • Bibliography
  • Index
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