Foliations and the Geometry of 3-Manifolds
Author(s): Calegari (Author)
- Publisher: ACADEMIC
- Publication Date: 12 July 2007
- Edition: Illustrated
- Language: English
- Print length: 378 pages
- ISBN-10: 0198570082
- ISBN-13: 9780198570080
Book Description
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.
Editorial Reviews
Review
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
Review
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds.
Review
"In fact the book is written in such a way that probably every reader with some interest in geometry will be able to find something interesting for him/her."--Mathematical Reviews
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