This text on contact topology is a 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.Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums.This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.
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