Convexity Properties of Hamiltonian Group Actions Paperback / softback
by Victor Guillemin, Reyer Sjamaar
Part of the CRM Monograph Series series
Paperback / softback
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Description
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.
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Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:82 pages
- Publisher:American Mathematical Society
- Publication Date:30/09/2006
- Category:
- ISBN:9780821842362
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:82 pages
- Publisher:American Mathematical Society
- Publication Date:30/09/2006
- Category:
- ISBN:9780821842362