An Introduction to Contact Topology / Edition 1

by Hansjörg Geiges

Overview

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.

Product Details

ISBN-13:	9780521865852
Publisher:	Cambridge University Press
Publication date:	03/13/2008
Series:	Cambridge Studies in Advanced Mathematics , #109
Edition description:	New Edition
Pages:	458
Product dimensions:	6.30(w) x 9.09(h) x 1.42(d)

About the Author

Hansjörg Geiges is Professor of Mathematics in the Mathematisches Institut at Universität zu Köln.

Table of Contents

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.

Editorial Reviews

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

From the Publisher