Foliations and the geometry of 3-manifolds

✍ Scribed by Danny Calegari

• Book ID: 127456511
• Publisher: Clarendon
• Year: 2007
• Tongue: English
• Weight: 3 MB
• Series: Oxford mathematical monographs
• Category: Library
• City: Oxford
• ISBN: 1435620941

✦ Synopsis

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.