Symplectic Topology and Floer Homology 2 Volume Hardback Set

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.

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.