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Foliations and the Geometry of 3-Manifolds

Foliations and the Geometry of 3-Manifolds by Danny Calegari
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This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especiallyin 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Clarendon Press; May 2007
378 pages; ISBN 9780191524639
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Title: Foliations and the Geometry of 3-Manifolds
Author: Danny Calegari