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Floer Homology Groups in Yang-Mills Theory

Floer Homology Groups in Yang-Mills Theory

Part of Cambridge Tracts in Mathematics

  • Author: S. K. Donaldson, Imperial College of Science, Technology and Medicine, London
  • Date Published: March 2002
  • availability: Available
  • format: Hardback
  • isbn: 9780521808033

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  • The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.

    • Written by a Fields Medallist
    • A modern account that sets the theory in the context of current work
    • Has many applications, such as Quantum Field Theory
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    Reviews & endorsements

    '… relatively short but very infomative, modern and clearly written … I stronly recommend the book to both specialists and graduate students'. S. Merkulov, Proceedings of the Edinburgh Mathematical Society

    '… a compact but very readable account.' Mathematika

    '… gives a nice account of the theory of an interesting topic in contemporary geometry and topology. It can be strongly recommended …'. EMS Newsletter

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    Product details

    • Date Published: March 2002
    • format: Hardback
    • isbn: 9780521808033
    • length: 246 pages
    • dimensions: 226 x 169 x 18 mm
    • weight: 0.48kg
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Basic material
    3. Linear analysis
    4. Gauge theory and tubular ends
    5. The Floer homology groups
    6. Floer homology and 4-manifold invariants
    7. Reducible connections and cup products
    8. Further directions.

  • Author

    S. K. Donaldson, Imperial College of Science, Technology and Medicine, London

    Assisted by

    M. Furuta

    D. Kotschick

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