LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	516.35
Title	Torus Actions on Symplectic Manifolds ([EBook]) / by Michèle Audin.
Author	Audin, Michèle
Other name(s)	SpringerLink (Online service)
Edition statement	Second revised edition.
Publication	Basel : Birkhäuser , 2004.
Physical Details	VIII, 328 pages : online resource.
Series	Progress in mathematics 0743-1643 ; ; 93
ISBN	9783034879606
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-7960-6
Links to Related Works	Subject References: Algebraic Geometry . Algebraic Topology . Differential Geometry . Hamiltonian systems . Mathematics . Symplectic manifolds . Authors: Audin, Michèle . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 516.35 .

Catalogue Display

Torus Actions on Symplectic Manifolds

Reviews