Convexity Properties of Hamiltonian Group Actions

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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.
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Product Details

  • ISBN-13: 9780821839188
  • Publisher: American Mathematical Society
  • Publication date: 11/28/2005
  • Series: CRM Monograph Series
  • Pages: 88
  • Product dimensions: 7.00 (w) x 10.20 (h) x 0.50 (d)

Table of Contents

Ch. 1 The convexity theorem for Hamiltonian G-spaces 7
Ch. 2 A constructive proof of the non-abelian convexity theorem 21
Ch. 3 Some elementary examples of the convexity theorem 31
Ch. 4 Kahler potentials and convexity 55
Ch. 5 Applications of the convexity theorem 71
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