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Item Details
| Title:
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CONVEXITY PROPERTIES OF HAMILTONIAN GROUP ACTIONS
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| By: |
Victor Guillemin, Reyer Sjamaar |
| Format: |
Paperback |
| List price:
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£101.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821842366 |
| ISBN 13: |
9780821842362 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 September, 2006 |
| Series: |
CRM Monograph Series (Z) |
| Pages: |
82 |
| Description: |
Presents a monograph on convexity properties of moment mappings in symplectic geometry. This book reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). |
| Synopsis: |
This is a monograph on convexity properties of moment mappings in symplectic geometry. The fundamental result in this subject is the Kirwan convexity theorem, which describes the image of a moment map in terms of linear inequalities. This theorem bears a close relationship to perplexing old puzzles from linear algebra, such as the Horn problem on sums of Hermitian matrices, on which considerable progress has been made in recent years following a breakthrough by Klyachko. The book presents a simple local model for the moment polytope, valid in the ""generic"" case, and an elementary Morse-theoretic argument deriving the Klyachko inequalities and some of their generalizations. It reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu).Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel su This volume is recommended for independent study and is suitable for graduate students and researchers interested in symplectic geometry, algebraic geometry, and geometric combinatorics.Information for our distributors: Titles in this series are co-published with the Centre de Recherches Mathematiques. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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