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| Introductory preface How I have （re-）written this Acknowledgements What I have written in this Ⅰ. Smooth Lie group Ⅰ.1. Generalities Ⅰ.2. Equivariant tubular neighborhoods and orbit types decomposition Ⅰ.3. Examples： S1-actions on manifolds of dimension 2 and 3 Ⅰ.4. Appendix： Lie groups， Lie algebras， homogeneous spacesExercises Ⅱ. Symplectie manifolds Ⅱ.1. What 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 mapp ing 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 fiat connections Ⅴ.3. Construction of commuting functions on M Ⅴ.4. Appendix： connections on principal bundles Exercises Ⅵ. Equivariant cohomology and the Duistermaat-tteckman 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 Ⅷ.2. Symplectic reduction and convex polyhedra Ⅶ.3. Cohomology of Ⅶ.4. Complex toric surfaces Exercises Ⅷ. Hamiltonian circle actions on manifolds of dimension Ⅷ.1. Symplectic S-actions， generalities Ⅷ.2. Periodic Hamiltonians on 4-dimensional manifolds Exercises Bibliography Index |
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