图书简介

Volume 1: Preface; Part I. Hamiltonian Dynamics and Symplectic Geometry: 1. Least action principle and the Hamiltonian mechanics; 2. Symplectic manifolds and Hamilton’s equation; 3. Lagrangian submanifolds; 4. Symplectic fibrations; 5. Hofer’s geometry of Ham(M, ω); 6. C0-Symplectic topology and Hamiltonian dynamics; Part II. Rudiments of Pseudo-Holomorphic Curves: 7. Geometric calculations; 8. Local study of J-holomorphic curves; 9. Gromov compactification and stable maps; 10. Fredholm theory; 11. Applications to symplectic topology; References; Index. Volume 2: Preface; Part III. Lagrangian Intersection Floer Homology: 12. Floer homology on cotangent bundles; 13. Off-shell framework of Floer complex with bubbles; 14. On-shell analysis of Floer moduli spaces; 15. Off-shell analysis of the Floer moduli space; 16. Floer homology of monotone Lagrangian submanifolds; 17. Applications to symplectic topology; Part IV. Hamiltonian Fixed Point Floer Homology: 18. Action functional and Conley–Zehnder index; 19. Hamiltonian Floer homology; 20. Pants product and quantum cohomology; 21. Spectral invariants: construction; 22. Spectral invariants: applications; Appendix A. The Weitzenböck formula for vector valued forms; Appendix B. Three-interval method of exponential estimates; Appendix C. Maslov index, Conley–Zehnder index and index formula; References; Index.

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