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Overview"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." Full Product DetailsAuthor: Victor Guillemin , Reyer SjamaarPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: Weight: 0.210kg ISBN: 9780821842362ISBN 10: 0821842366 Pages: 82 Publication Date: 30 September 2006 Audience: College/higher education , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsIntroduction The convexity theorem for Hamiltonian $G$-spaces A constructive proof of the non-abelian convexity theorem Some elementary examples of the convexity theorem Kahler potentials and convexity Applications of the convexity theorem Bibliography.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |