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.