An Introduction to Contact Topology

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.

• 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