Symplectic topology as the geometry of action functional . I-relative floer theory on the cotangent bundle

Journal of Differential Geometry

Volumn 46, Issue 3, 1997, Pages 499-577

  Oh, Yong Geun ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031184688     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214459976     Document Type: Article

References (56)

1. V. I. Arnold, Sur une propriété topologique des applications globallmant canoniques de la mécanique classique, C. R. Acad. Sci. Paris 261 (1965) 3719-3722.
2. V. I. Arnold, Characteristic class entering in quantization conditions, Functional Anal. Appl. 1 (1967) 1-8.
3. V. I. Arnold, The Sturm theorems and symplectic geometry, Functional Anal. Appl. 19 (1985) 251-259.
4. V. Benci, On critical point theory for indefinite functionals in the presence of symmetries, Trans. Amer. Math. Soc. 274 (1982) 533-572.
5. V. Benci & R. Rabinowitz, Critical point theorems for indefinite functionals, Invent. Math. 52 (1979) 241-273.
6. M. Betz & R. Cohen, Graph moduli spaces and cohomology operations, Turkish J. Math. 18 (1995) 23-41.
7. M. Betz & J. Rade, Products and relations in symplectic Floer homology, Preprint.
8. M. Chaperon, Quelques questiones de geometrie symplectique, Astérisque 105-106 (1983) 231-249.
9. Y. Chekanov, Hofer’s symplectic energy and Lagrangian intersections, Publ. Newton Inst., Cambridge University Press 8 (1996) 296-306.
10. S. Cappell, R. Lee & E. Miller, On the Maslov index, Comm. Pure Appl. Math. 47 (1984) 121-186.
11. C. Conley & E. Zehnder, The Birkhoff-Lewis fixed point theorem and a conjecture by V.I. Arnold, Invent. Math. 73 (1983) 33-49.
12. Y. Eliashberg, A theorem on the structure of wave fronts and applications in symplectic topology, Functional Anal. Appl. 21 (1987) 227-232.
13. Y. Eliashberg, H. Hofer & D. Salamon, Lagrangian intersections in contact geometry, J. Geom. Funct. Anal. 5 (1995) 244-269.
14. Y. Eliashberg & J. -C. Sikorav, private discussions.
15. I. Ekeland & H. Hofer, Symplectic topology and Hamiltonian dynamics, Math. Z. 200 (1990) 355-378.
16. I. Ekeland & H. Hofer, Symplectic topology and Hamiltonian dynamics. II, Math. Z. 203 (1990) 553-567.
17. A. Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775-813.
18. A. Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988) 513-547.
19. A. Floer, A relative Morse index for the symplectic action, Comm.Pure Appl. Math. 41 (1988) 393-407.
20. A. Floer, Witten’s complex and infinite dimensional Morse theory, J. Differential Geom. 30 (1989) 207-221.
21. A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989) 575-611.
22. A. Floer & H. Hofer, Coherent orientations for periodic orbit problems in symplectic geometry, Math. Z. 212 (1993) 13-38.
23. n, Math. Z. 215 (1994) 37-88.
24. A. Floer, H. Hofer, & D. Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995) 251-292.
25. K. Fukaya, Morse homotopy and its quantization, to appear in Proc. Georgia Topology Conference.
26. K. Fukaya, Morse theory and topological field theory, to appear in Suugaku Expositions.
27. K. Fukaya & Y. -G. Oh, Zero-loop open string in the cotangent bundle and Morse homotopy, to appear in Asian J. Math.
28. M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 81 (1985) 307-347.
29. H. Hofer, Lagrangian embeddings and critical point theory, Ann. Inst. H. Poincaré, Anal. Non Linéaire, 2 (1985) 407-462.
30. H. Hofer, On the topological properties of symplectic maps, Proc. Royal Soc. Edinburgh 115 (1990) 25-38.
31. H. Hofer & E. Zehnder, Symplectic invariants and hamiltonian dynamics, Birkhàuser Adv. Texts, Boston, 1994.
32. F. Lalonde & D. McDuff, The geometry of symplectic energy, Ann. Of Math. 141 (1995) 349-371.
33. ∞ -geometry: energy and stability of Hamiltonian flows. I, II, to appear in Invent. Math.
34. F. Laudenbach & J. C. Sikorav, Persistence d’intersections avec la section mulle au conurs d’une isotopie Hamiltonienne dans un fibre cotangent, Invent. Math. 82 (1985) 349-357.
35. D. McDuff, Elliptic methods in symplectic geometry, Bull. Amer. Math. Soc. 23 (2) (1990) 311-358.
36. D. McDuff, Symplectic manifolds with contact type boundaries, Invent. Math. 103 (1991), 651-671.
37. J. Milnor, Lectures on the H-cobordism theorem, Princeton University Press, Princeton, New Jersey, 1965.
38. Y. -G. Oh, Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks I, Comm. Pure Appl. Math. 46 (1993) 949-994.
39. Y. -G. Oh, On the structure of pseudo-holomorphic discs with totally real boundary conditions, to appear in J. Geom. Anal.
40. Y. -G. Oh, Fred, holm theory of holomorphic discs under the perturbation of boundary condition, Math. Z. 222 (1996) 505-520.
41. n, Internat. Math. Res. Notices, No 7 (1996) 305-346.
42. Y. -G. Oh, Relative Floer and quantum cohomology and the symplectic topology of Lagrangian submanifolds, Publ. Newton Inst., Cambridge University Press, 8 (1996) 201-267.
43. Y. -G. Oh, Symplectic topology as the geometry of action functional. II, submitted.
44. K. Ono, Lagrangian intersection under Leqendrian deformations, Invent. Math. 119 (1995) 519-537.
45. L. Polterovich, Symplectic displacement energy for Lagrangian submanifolds, Er-godic Theory Dynamical Systems 13 (1993) 357-367.
46. M. Poźniak, Floer homology, Novikov rings and clean intersections, Thesis, University of Warwick, 1994.
47. S. Piunikhin, D. Salamon, & M. Schwarz, Symplectic Floer-Donaldson theory and quantum cohomology, Publ. Newton Inst., Cambridge University Press, 8 (1996) 171-200.
48. P. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS, Regional Conf. Ser. in Math. 65 Amer. Math. Soc., 1986.
49. J. Robbin & D. Salamon, The Maslov index for paths, Topology 32 (1993) 827-844.
50. J. Robbin & D. Salamon, The spectral flow and the Maslov index, Bull. London Math. Soc. 27 (1995) 1-33.
51. M. Schwarz, Morse homology, Progr. Math. Vol. III, Birkhàuser, 1993.
52. M. Schwarz, Thesis, ETH, Zürich, 1995.
53. J. -C. Sikorav, Problèmes d’intersections et de points fixes en géométrie hamiltoni-enne, Comment. Math. Helv. 62 (1987) 62-73.
54. D. Salamon & E. Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992) 1303-1360.
55. D. Theret, Thèse, Université Dennis Diderot (Paris VII), 1995.
56. C. Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992) 685-710.