Yong-Geun Oh is Director of the IBS Center for Geometry and Physics and is Professor in the Department of Mathematics at POSTECH (Pohang University of Science and Technology) in Korea. He was also Professor in the Department of Mathematics at the University of Wisconsin, Madison. He is a member of the KMS, the AMS, the Korean National Academy of Sciences, and the inaugural class of AMS Fellows. In 2012 he received the Kyung-Ahm Prize for Science in Korea.
Inhaltsangabe
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, ¿) 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.
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, ¿) 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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