An Introduction to Contact Topology

This self-contained text is an introduction to contact topology. Ideal for graduate courses on contact geometry, and as a reference for researchers.

Hansjörg Geiges (Author)

9780521865852, Cambridge University Press

Hardback, published 13 March 2008

458 pages, 85 b/w illus.
23.1 x 16 x 3.6 cm, 0.77 kg

'… a fundamental monograph … can be strongly recommended for graduate students and is indispensable for specialists in the field.' EMS Newsletter

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.

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 Poincaré lemma
Appendix B. Time-dependent vector fields
References
Notation Index
Author Index
Subject Index.

Subject Areas: Topology [PBP]