An Introduction to Contact Topology

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.

• First text to give a comprehensive introduction to contact geometry, with thorough discussion of all basic methods of the subject
• Long introductory chapter on the historical roots of contact geometry and its connection with physics, Riemannian geometry, and geometric topology
• Proofs of many folklore results and careful presentation of all fundamental results in the subject
• Detailed exposition of Eliashberg's classification of overtwisted contact structures