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  3. An Introduction to Contact Topology
  • Cited by 388
Publisher:
Cambridge University Press
Online publication date:
November 2009
Print publication year:
2008
Online ISBN:
9780511611438
DOI:
https://doi.org/10.1017/CBO9780511611438
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
Cambridge Studies in Advanced Mathematics (109)
Information

Book description

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.

Reviews

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

Source: EMS Newsletter

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