Torus Actions on Symplectic Manifolds

1. Front Matter

   Pages i-viii

   PDF

2. Introductory Preface

   • Michèle Audin

   Pages 1-8

3. Smooth Lie Group Actions on Manifolds

   • Michèle Audin

   Pages 9-42

4. Symplectic Manifolds

   • Michèle Audin

   Pages 43-69

5. Symplectic and Hamiltonian Group Actions

   • Michèle Audin

   Pages 71-104

6. Morse Theory for Hamiltonians

   • Michèle Audin

   Pages 105-146

7. Moduli Spaces of Flat Connections

   • Michèle Audin

   Pages 147-176

8. Equivariant Cohomology and the Duistermaat-Heckman Theorem

   • Michèle Audin

   Pages 177-224

9. Toric Manifolds

   • Michèle Audin

   Pages 225-270

10. Hamiltonian Circle Actions on Manifolds of Dimension 4

    • Michèle Audin

    Pages 271-310

11. Back Matter

    Pages 311-325

    PDF

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.

• Algebraic topology
• Lie group
• Torus manifolds
• cohomology
• homology
• manifold
• moduli space
• symplectic geometry
• symplectic manifold

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)

• Institut de Recherche Mathématique Avancée, Université Louis Pasteur, Strasbourg Cedex, France

  Michèle Audin

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