Author | Audin, Michรจle. author |
---|---|
Title | Torus Actions on Symplectic Manifolds [electronic resource] / by Michรจle Audin |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2004 |
Edition | Second revised edition |
Connect to | http://dx.doi.org/10.1007/978-3-0348-7960-6 |
Descript | VIII, 328 p. online resource |
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