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An Introduction to Contact Topology

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: March 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521865852

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  • 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.

    • First text to give a comprehensive introduction to contact geometry, with thorough discussion of all basic methods of the subject
    • Long introductory chapter on the historical roots of contact geometry and its connection with physics, Riemannian geometry, and geometric topology
    • Proofs of many folklore results and careful presentation of all fundamental results in the subject
    • Detailed exposition of Eliashberg's classification of overtwisted contact structures
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    Reviews & endorsements

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

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    Product details

    • Date Published: March 2008
    • format: Hardback
    • isbn: 9780521865852
    • length: 458 pages
    • dimensions: 231 x 160 x 36 mm
    • weight: 0.77kg
    • contains: 85 b/w illus.
    • availability: Available
  • 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.

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    An Introduction to Contact Topology

    Hansjörg Geiges

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  • Author

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

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