Convexity Properties of Hamiltonian Group Actions (CRM Monograph Series)

Convexity Properties of Hamiltonian Group Actions (CRM Monograph Series)

By: Reyer Sjamaar (author), Victor Guillemin (author)Paperback

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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.

Contents

Introduction 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.

Product Details

  • ISBN13: 9780821842362
  • Format: Paperback
  • Number Of Pages: 82
  • ID: 9780821842362
  • ISBN10: 0821842366

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