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Geometry of Low-Dimensional Manifolds

Geometry of Low-Dimensional Manifolds
Symplectic Manifolds and Jones-Witten Theory

Volume 2


Part of London Mathematical Society Lecture Note Series

Dusa McDuff, H. Hofer, A. B. Givental, Yakov Eliashberg, Edward Witten, Lisa Jeffrey, N. J. Hitchin, Robion Kirby, Paul Melvin, M. F. Atiyah, I. R. Aitchison, J. H. Rubinstein, C. B. Thomas, R. C. Kirby, L. R. Taylor
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  • Date Published: January 1991
  • availability: Available
  • format: Paperback
  • isbn: 9780521400015

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About the Authors
  • This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects interact (for example: topology, differential and algebraic geometry and mathematical physics). The workshop brought together a number of distinguished figures to give lecture courses and seminars in these subjects; the volume that has resulted is the only expository source for much of the material, and will be essential for all research workers in geometry and mathematical physics.

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    Product details

    • Date Published: January 1991
    • format: Paperback
    • isbn: 9780521400015
    • length: 260 pages
    • dimensions: 230 x 152 x 17 mm
    • weight: 0.319kg
    • availability: Available
  • Table of Contents

    Names of Participants
    Part I. Symplectic Geometry:
    1. Introduction
    2. Rational and ruled symplectic 4-manifolds Dusa McDuff
    3. Symplectic capacities H. Hofer
    4. The nonlinear Maslov index A. B. Givental
    5. Filling by holomorphic discs and its applications Yakov Eliashberg
    Part II. Jones/Witten Theory:
    6. Introduction
    7. New results in Chern-Simons theory Edward Witten, notes by Lisa Jeffrey
    8. Geometric quantization of spaces of connections N. J. Hitchin
    9. Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C) Robion Kirby and Paul Melvin
    10. Representations of braid groups M. F. Atiyah, notes by S. K. Donaldson
    Part III. Three-Dimensional Manifolds:
    11. Introduction
    12. An introduction to polyhedral metrics of non-positive curvature on 3-manifolds I. R. Aitchison and J. H. Rubinstein
    13. Finite groups of hyperbolic isometries C. B. Thomas
    14. Pin structures on low-dimensional manifolds R. C. Kirby and L. R. Taylor.

  • Editors

    S. K. Donaldson, University of Oxford

    C. B. Thomas, University of Cambridge


    Dusa McDuff, H. Hofer, A. B. Givental, Yakov Eliashberg, Edward Witten, Lisa Jeffrey, N. J. Hitchin, Robion Kirby, Paul Melvin, M. F. Atiyah, I. R. Aitchison, J. H. Rubinstein, C. B. Thomas, R. C. Kirby, L. R. Taylor

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