Torus Actions on Symplectic Manifolds: 93 (Progress in Mathematics, 93) - Hardcover

Audin, Michele

Hardcover

ISBN 10: 3764321768 ISBN 13: 9783764321765

Verlag: Birkhäuser, 2004

Inhaltsangabe

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.

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From the reviews:

“Through careful writing, this revised edition achieves much more than that volume, and can be considered, in fact, a new and improved book. The second edition contains more material, and includes several new results and techniques. Topics included in the first edition are now presented more thoroughly, with more results, illustrated by well-chosen examples, and many new exercises. The author has systematically addressed suggestions made in the review of the first edition. The book is nicely written, and is a good reference book. By including detailed proofs, illuminating examples and figures, and numerous exercises, the author has made this book a suitable text for a graduate course, especially one centered on Hamiltonian torus actions and their applications.”(MATHEMATICAL REVIEWS)

Reseña del editor

The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, 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 results, it contains much more material, in particular lots of new examples and exercises.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2004
• Sprache: Englisch
• ISBN 10: 3764321768
• ISBN 13: 9783764321765
• Einband: Tapa dura
• Auflage: 2
• Anzahl der Seiten: 342
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar