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.
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Book Description
Editorial Reviews
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"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
"...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
Book Description
This is an accessible introduction to some of the fundamental connections between differential geometry, Lie groups, and integrable Hamiltonian systems. It 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.The specific goal of the book is to show how the theory of loop groups can be used to study harmonic maps. By concentrating on the main ideas and examples, the book leads up to topics of current research.
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Inside This Book
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First Sentence:
We assume that the reader is familiar with the idea of a (smooth) manifold. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite uniton number, harmonic map equation, minimal uniton number, corresponding harmonic map, twisted loop group, harmonic maps, bibliographical comments, dressing transformations, primitive maps, dressing action, loop groups, loop algebras, soliton equations, finite type, integrable systems, middle factor, isotropy subgroup, flag manifold, old action, holomorphic section, big cell, harmonic sequence, holomorphic maps, symmetric space, invariant vector field Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reality Assumption, Kac-Moody Lie New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We assume that the reader is familiar with the idea of a (smooth) manifold. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite uniton number, harmonic map equation, minimal uniton number, corresponding harmonic map, twisted loop group, harmonic maps, bibliographical comments, dressing transformations, primitive maps, dressing action, loop groups, loop algebras, soliton equations, finite type, integrable systems, middle factor, isotropy subgroup, flag manifold, old action, holomorphic section, big cell, harmonic sequence, holomorphic maps, symmetric space, invariant vector field Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reality Assumption, Kac-Moody Lie New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 28
books:
See all 28 books this book cites
- Harmonic Maps and Integrable Systems (Aspects of Mathematics) by Allan P. Fordy in Back Matter (1), and Back Matter (2)
- Differential Geometry (Proceedings of Symposia in Pure Mathematics ; V. 54 Part 1, 2, 3) (Pt.1-3) by Robert Greene in Back Matter
- Lectures on Differential Geometry by Sholomo Sternberg in Back Matter
- Symplectic Techniques in Physics by Victor Guillemin in Back Matter
- Morse Theory (Annals of Mathematic Studies AM-51) by John Milnor in Back Matter
See all 28 books this book cites
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