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Foliations and the Geometry of 3-Manifolds

Foliations and the Geometry of 3-Manifolds
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US$ 149.99
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. - ;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, especially in

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. - ;This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurstone'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, especially in

1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combonatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects. - Bulletin Bibliographique;The book is extremely well written and it is very pleasant to read. The definitions and the statements of the results are presented clearly, with a lot of illustrations and judicious examples ... This book is unique on most of the topics that it contains, and, for this and for other reasons, it constitutes a very important contribution to low-dimensional topology literature. - Anthanase Papadopoulos, Zentralblatt Math

Oxford University Press, UK; May 2007
378 pages; ISBN 9780191524639
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