Geiges H. An Introduction to Contact Topology

Cambridge University Press, 2008. — 458 p. — (Cambridge Studies in Advanced Mathematics 109). — ISBN13: 978-0-511-37885-0.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.Facets of contact geometry
Contact manifolds
Knotsincontact 3–manifolds
Contact structures on 3–manifolds
Symplectic fillings and convexity
Contact surgery
Further constructions of contact manifolds
Contact structures on 5–manifolds
Appendixes
The generalised Poincar´e lemma
Time-dependent vector fields