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Harmonic Maps, Loop Groups, and Integrable Systems

Part of London Mathematical Society Student Texts

Author: Martin A. Guest, Tokyo Metropolitan University

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

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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
Preface
Acknowledgements
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
References
Index.
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Author
Martin A. Guest, Tokyo Metropolitan University