Introduction to Contact Topology 1E - Geiges, Hansjörg

Introduction to Contact Topology 1E

Hansjörg Geiges

Yayınevi: Cambridge University Press

Yayın tarihi: 03/2008

ISBN: 9780521865852

Ciltli | İngilizce | 456 Sayfa | 152 mm x 228 mm

Tür: Matematik-İstatistik

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Cambridge Studies in Advanced Mathematics Series No.109

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. 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.

Contents:
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

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