# The Hyperbolization Theorem for Fibered 3-Manifolds

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*Jean-Pierre Otal*

A co-publication of the AMS and Société Mathématique de France

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(unpublished) proof, though the double limit theorem is dealt with in a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 & Endorsements

The book is very well written … completely self-contained …

-- Mathematical Reviews