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Foliations and the Geometry of 3-Manifolds
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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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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.

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.
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