Torus Actions on Symplectic Manifolds

Michèle Audin

ISBN 10: 3764321768 / ISBN 13: 9783764321765

Verlag: Springer, Basel, Birkhäuser Basel, Birkhäuser Sep 2004, 2004

Beschreibung

This item is printed on demand - it takes 3-4 days longer - Neuware -How I have (re-)written this book The book the reader has in hand was supposed to be a new edition of [14]. I have hesitated quite a long time before deciding to do the re-writing work-the first edition has been sold out for a few years. There was absolutely no question of just correcting numerous misprints and a few mathematical errors. When I wrote the first edition, in 1989, the convexity and Duistermaat-Heckman theorems together with the irruption of toric varieties on the scene of symplectic geometry, due to Delzant, around which the book was organized, were still rather recent (less than ten years). I myself was rather happy with a small contribution I had made to the subject. I was giving a post-graduate course on all that and, well, these were lecture notes, just lecture notes. By chance, the book turned out to be rather popular: during the years since then, I had the opportunity to meet quite a few people(1) who kindly pretended to have learnt the subject in this book. However, the older book does not satisfy at all the idea I have now of what a good book should be. So that this 'new edition' is, indeed, another book. 328 pp. Englisch.

Bestandsnummer des Verkäufers 9783764321765

Bibliografische Details

• Titel: Torus Actions on Symplectic Manifolds
• Verlag: Springer, Basel, Birkhäuser Basel, Birkhäuser Sep 2004
• Erscheinungsjahr: 2004
• Sprache: Englisch
• ISBN-10: 3764321768
• ISBN-13: 9783764321765
• Einband: Buch
• Auflage: 2. Auflage
• Zustand: Neu
• Abmessungen: 239B x 161 H x 24 T Millimeter Breite: 239 mm, Höhe: 161 mm, Tiefe: 24 mm
• Gewicht: 696 Gramm

Über diesen Titel

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.

Críticas

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)