Convexity Properties of Hamiltonian Group Actions (CRM Monograph Series) - Softcover

Guillemin, Victor; Sjamaar, Reyer

Softcover

ISBN 10: 0821842366 ISBN 13: 9780821842362

Publisher: American Mathematical Society, 2007

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2007
• Language: English
• ISBN 10: 0821842366
• ISBN 13: 9780821842362
• Binding: Paperback
• Number of pages: 82