Logo - springer
Slogan - springer

Birkhäuser - Birkhäuser Mathematics | Torus Actions on Symplectic Manifolds

Torus Actions on Symplectic Manifolds

Series: Progress in Mathematics, Vol. 93

Audin, Michèle

2nd revised ed. 2004, VIII, 328 p.

A product of Birkhäuser Basel
Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$109.00

(net) price for USA

ISBN 978-3-0348-7960-6

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$139.00

(net) price for USA

ISBN 978-3-7643-2176-5

free shipping for individuals worldwide

The book title is in reprint. You can already preorder it.


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$139.00

(net) price for USA

ISBN 978-3-0348-9637-5

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

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.

Content Level » Research

Keywords » Algebraic topology - Lie group - Torus manifolds - cohomology - homology - manifold - moduli space - symplectic geometry - symplectic manifold

Related subjects » Birkhäuser Mathematics

Table of contents 

Introductory preface.- How I have (re-)written this book.- Acknowledgements.- What I have written in this book.- I. Smooth Lie group actions on manifolds.- I.1. Generalities.- I.2. Equivariant tubular neighborhoods and orbit types decomposition.- I.3. Examples: S 1-actions on manifolds of dimension 2 and 3.- I.4. Appendix: Lie groups, Lie algebras, homogeneous spaces.- Exercises.- II. Symplectic manifolds.- II.1What is a symplectic manifold?.- II.2. Calibrated almost complex structures.- II.3. Hamiltonian vector fields and Poisson brackets.- Exercises.- III. Symplectic and Hamiltonian group actions.- III.1. Hamiltonian group actions.- III.2. Properties of momentum mappings.- III.3. Torus actions and integrable systems.- Exercises.- IV. Morse theory for Hamiltonians.- IV.1. Critical points of almost periodic Hamiltonians.- IV.2. Morse functions (in the sense of Bott).- IV.3. Connectedness of the fibers of the momentum mapping.- IV.4. Application to convexity theorems.- IV.5. Appendix: compact symplectic SU(2)-manifolds of dimension 4.- Exercises.- V. Moduli spaces of flat connections.- V.1. The moduli space of fiat connections.- V.2. A Poisson structure on the moduli space of flat connections.- V.3. Construction of commuting functions on M.- V.4. Appendix: connections on principal bundles.- Exercises.- VI. Equivariant cohomology and the Duistermaat-Heckman theorem.- VI.1. Milnor joins, Borel construction and equivariant cohomology.- VI.2. Hamiltonian actions and the Duistermaat-Heckman theorem.- VI.3. Localization at fixed points and the Duistermaat-Heckman formula.- VI.4. Appendix: some algebraic topology.- VI.5. Appendix: various notions of Euler classes.- Exercises.- VII. Toric manifolds.- VII.1. Fans and toric varieties.- VII.2. Symplectic reduction and convex polyhedra.- VII.3. Cohomology of X ?.- VII.4. Complex toric surfaces.- Exercises.- VIII. Hamiltonian circle actions on manifolds of dimension 4.- VIII.1. Symplectic S 1-actions, generalities.- VIII.2. Periodic Hamiltonians on 4-dimensional manifolds.- Exercises.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Algebraic Geometry.