© 2004

Torus Actions on Symplectic Manifolds


Part of the Progress in Mathematics book series (PM, volume 93)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Michèle Audin
    Pages 1-8
  3. Michèle Audin
    Pages 9-42
  4. Michèle Audin
    Pages 43-69
  5. Michèle Audin
    Pages 71-104
  6. Michèle Audin
    Pages 105-146
  7. Michèle Audin
    Pages 147-176
  8. Michèle Audin
    Pages 225-270
  9. Back Matter
    Pages 311-325

About this book


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

Authors and affiliations

  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis PasteurStrasbourg CedexFrance

Bibliographic information

  • Book Title Torus Actions on Symplectic Manifolds
  • Authors Michèle Audin
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI
  • Copyright Information Birkhäuser Verlag 2004
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-2176-5
  • Softcover ISBN 978-3-0348-9637-5
  • eBook ISBN 978-3-0348-7960-6
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 2
  • Number of Pages VIII, 328
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
    Differential Geometry
    Algebraic Topology
  • Buy this book on publisher's site


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)