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- Title Foliations and the Geometry of 3-Manifolds
- Author(s) Danny Calegari
- Publisher: Clarendon Press; Illustrated edition (July 12, 2007)
- Permission: "This book was published in May 2007 by Oxford University Press in their Mathematical Monograph series. The .pdf is available for download here with their permission, although I encourage you to buy a physical copy if you find this version useful."
- Hardcover: 352 pages
- eBook: PDF (371 pages)
- Language: English
- ISBN-10: 0198570082
- ISBN-13: 978-0198570080
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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, 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.
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.
About the Authors- Danny Calegari is a mathematician who is currently a professor of mathematics at the University of Chicago. His research interests include geometry, dynamical systems, low-dimensional topology, and geometric group theory.
- Geometry and Topology
- Computer Graphics
- Computational and Algorithmic Mathematics
- Applied Mathematics

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