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An Introduction to Contact Topology (Cambridge Studies in Advanced Mathematics)
Posted on 2010-04-16
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Author: Hansj?rg Geiges
Publisher: Cambridge University Press (2008) Binding: Hardcover, 456 pages pricer: $90.00 ISBN-10: 0521865859 editorialreviews This text on contact topology is the first comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology where the focus mainly on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums.
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