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Harmonic Maps, Loop Groups, and Integrable Systems

Harmonic Maps, Loop Groups, and Integrable Systems

$61.99 (P)

Part of London Mathematical Society Student Texts

  • Date Published: January 1997
  • availability: Available
  • format: Paperback
  • isbn: 9780521589321

$ 61.99 (P)

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About the Authors
  • This is an accessible introduction to some of the fundamental connections among differential geometry, Lie groups, and integrable Hamiltonian systems. The text demonstrates how the theory of loop groups can be used to study harmonic maps. By concentrating on the main ideas and examples, the author leads up to topics of current research. The book is suitable for students who are beginning to study manifolds and Lie groups, and should be of interest both to mathematicians and to theoretical physicists as well.

    • Deals with the intersection of three important areas: harmonic maps, loop groups, and integrable systems
    • Guides the reader from elementary topics to current research
    • Accessible: emphasises main ideas and examples
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    Reviews & endorsements

    "This is an accessible and very interesting text..." Monashefte fur Mathematik

    "...a very well written, easily accessible introduction to how loop group techniques are used in the description of harmonic maps from Riemann surfaces to compact Lie groups and compant symmetric spaces...The book presents in a unifying way a very nice introduction to a new part of harmonice map theory, is easily accessible, fun to read and has a modest price. It is an ideal text for a beginning graduate student and any newcomer to the field." Bulletin of the American Mathematical Society

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    Product details

    • Date Published: January 1997
    • format: Paperback
    • isbn: 9780521589321
    • length: 212 pages
    • dimensions: 229 x 153 x 13 mm
    • weight: 0.29kg
    • availability: Available
  • Table of Contents

    Part I. One-Dimensional Integrable Systems:
    1. Lie groups
    2. Lie algebras
    3. Factorizations and homogeneous spaces
    4. Hamilton's equations and Hamiltonian systems
    5. Lax equations
    6. Adler-Kostant-Symes
    7. Adler-Kostant-Symes (continued)
    8. Concluding remarks on one-dimensional Lax equations
    Part II. Two-Dimensional Integrable Systems:
    9. Zero-curvature equations
    10. Some solutions of zero-curvature equations
    11. Loop groups and loop algebras
    12. Factorizations and homogeneous spaces
    13. The two-dimensional Toda lattice
    14. T-functions and the Bruhat decomposition
    15. Solutions of the two-dimensional Toda lattice
    16. Harmonic maps from C to a Lie group G
    17. Harmonic maps from C to a Lie group (continued)
    18. Harmonic maps from C to a symmetric space
    19. Harmonic maps from C to a symmetric space (continued)
    20. Application: harmonic maps from S2 to CPn
    21. Primitive maps
    22. Weierstrass formulae for harmonic maps
    Part III. One-Dimensional and Two-Dimensional Integrable Systems:
    23. From 2 Lax equations to 1 zero-curvature equation
    24. Harmonic maps of finite type
    25. Application: harmonic maps from T2 to S2
    26. Epilogue

  • Author

    Martin A. Guest, Tokyo Metropolitan University

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