An Introduction to Contact Topology [Hardcover]

This self-contained text is an introduction to contact topology. Ideal for graduate courses on contact geometry, and as a reference for researchers.This self-contained text is a comprehensive introduction to the subject of contact topology. The reader is led from the historical roots of contact geometry to striking recent applications in geometric and differential topology. Ideal for graduate courses on contact geometry, and as a reference for researchers.This self-contained text is a comprehensive introduction to the subject of contact topology. The reader is led from the historical roots of contact geometry to striking recent applications in geometric and differential topology. Ideal for graduate courses on contact geometry, and as a reference for researchers.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.Foreword; 1. Facets of Contact Geometry; 2. Contact Manifolds; 3. Knots in Contact 3-Manifolds; 4. Contact Structures on 3-Manifolds; 5. Symplectic Fillings and Convexity; 6. Contact Surgery; 7. Further Constructions of Contact Manifolds; 8. Contact Structures on 5-Manifolds; Appendix A. The generalised Poincar? lemma; Appendix B. Time-dependent vector fields; References; Notation Index;l½