Foliations and the Geometry of 3-Manifolds
- ISBN-10
- 0191524638
- ISBN-13
- 9780191524639
- Category
- Mathematics
- Pages
- 384
- Language
- English
- Published
- 2007-05-17
- Publisher
- Clarendon Press
- Author
- Danny Calegari
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.
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