Torus Actions on Symplectic Manifolds

By:

Michele Audin

Format:

Hardback

Series:

Progress in Mathematics

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Description

This is an extended second edition of "The Topology of Torus Actions on Symplectic Manifolds" published in this series in 1991. The material and references have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity theorems, it contains much more results, proofs and examples. Chapter I deals with Lie group actions on manifolds. In Chapters II and III, symplectic geometry and Hamiltonian group actions are introduced, especially torus actions and action-angle variables. The core of the book is Chapter IV which is devoted to applications of Morse theory to Hamiltonian group actions, including convexity theorems. As a family of examples of symplectic manifolds, moduli spaces of flat connections are discussed in Chapter V. Then, Chapter VI centers on the Duistermaat-Heckman theorem. In Chapter VII, a topological construction of complex toric varieties is presented, and the last chapter illustrates the introduced methods for Hamiltonian circle actions on 4-manifolds.

Release date NZ

September 27th, 2004

Author

Michele Audin

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational
Undergraduate

Edition

2nd revised ed. 2004

Illustrations

VIII, 328 p.

Pages

328

Series

Progress in Mathematics

Dimensions

155x235x23

ISBN-13

9783764321765

Product ID

5269307

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