Download PDF - On Arnold's conjecture for symplectic fixed pointsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On Arnold's conjecture for symplectic fixed points

Authors 1

Affiliations

  1. Department of Mathematics, Ochanomizu University, Otsuka, Tokyo 112, Japan

Bibliography

  1. M. Atiyah, V. Patodi and I. Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Phil. Soc. 77 (1975), 43-69, II, ibid. 78 (1975), 405-432.
  2. V. I. Arnold, Mathematical Methods in Classical Mechanics, Graduate Text in Mathematics 60, Springer Verlag.
  3. K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. (1997).
  4. M. Chaperon, Une idée du type géodesiques brisées, Comptes Rendues Paris 298 (1984), 293-296.
  5. Y. Chekanov, Hofer's symplectic energy and Lagrangian intersections, in: Contact and Symplectic Geometry, ed. by C. B. Thomas, Cambridge University Press, 1996; Lagrangian intersections, symplectic energy and areas of holomorphic curves, preprint.
  6. C. Conley and E. Zehnder, The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold, Invent. Math. 73 (1983), 33-49; Morse type index theory for flows and periodic solutions for Hamiltonian systems, Comm. Pure Appl. Math. 37 (1984), 207-253.
  7. A. Floer, Morse theory for lagrangian intersections, Journ. Differ. Geom. 28 (1988), 513-547; The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988), 775-813; A relative Morse index for the symplectic action, Comm. Pure Appl. Math. 41 (1988), 393-407; Witten's complex and infinite dimensional Morse theory, Journ. Differential Geom. 30 (1989), 207-221; Cup length estimate on lagrangian intersections, Comm. Pure Appl. Math. 42 (1989), 335-357.
  8. A. Floer, Holomorphic spheres and symplectic fixed points, Comm. Math. Phys. 120 (1989), 575-611.
  9. A. Floer and H. Hofer, Coherent orientations for periodic orbits problems in symplectic geometry, Math. Z. 212 (1993), 13-38.
  10. A. Floer, H. Hofer and D. Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. Journ. 80 (1995), 251-292.
  11. K. Fukaya, The symplectic S-cobordism conjecture: a summary, in: Geometry and Physics, ed. by J. E. Andersen, J. Dupont, H. Pedersen and A. Swann, Lecture Notes in Pure and Appl. Math. 184 (1997), 209-219.
  12. K. Fukaya and K. Ono, Arnold conjecture and Gromov-Witten invariant for general symplectic manifolds (announcement); Arnold conjecture and Gromov-Witten invariant, preprint, 1996.
  13. M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
  14. H. Hofer, Lagrangian embeddings and critical point theory, Ann. Inst. H. Poincaré, Anal. Non Linéaire 2 (1985), 407-462; Lusternik-Schnirelmann theory for Lagrangian intersections, ibid. 5 (1988), 465-499.
  15. H. Hofer and D. Salamon, Floer homology and Novikov rings, Floer memorial volume, ed. by H. Hofer, C. Taubes, A. Weinstein and E. Zehnder, 483-524, Birkhäuser 1995.
  16. M. Kontsevich, Enumeration of rational curves by torus actions, in: Moduli space of curves, ed. by H. Dijkgraaf, C. Faber, G. v. d.Geer, 335-368, Progress in Mathematics 129, Birkhäuser 1995.
  17. M. Kuranishi, New proof for the existence of locally free complete families of complex structures, in: Conference on Complex Analysis, 1996 Mineapolis, Springer-Verlag.
  18. F. Laudenbach and J.-C. Sikorav, Persistence d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent, Invent. Math. 82 (1985), 349-358.
  19. H. V. Lê and K. Ono, Symplectic fixed points, the Calabi invariant and Novikov homology, Topology 34 (1995), 155-176.
  20. H. V. Lê and K. Ono, Cup-length estimate for symplectic fixed points, in: Contact and Symplectic Geometry, 268-295, ed. by C. B. Thomas, Publication of the Newton Institute, Cambridge Univ. Press, 1996.
  21. J. Li and G. Tian, Virtual moduli cycles and Gromov-Witten invariants for general symplectic manifolds, preprint 1996.
  22. G. Liu and G. Tian, preprint 1996.
  23. D. McDuff, Elliptic methods in symplectic geometry, Bull. Amer. Math. Soc. 23 (1990), 311-358.
  24. D. McDuff and D. Salamon, J-holomorphic curves and quantum cohomology, University Lecture Ser., 6, Amer. Math. Soc. 1994.
  25. Y. G. Oh, Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks, I, Comm. Pure Appl. Math. 46 (1993), 949-994, II ibid. 46 (1993), 995-1012, III, in: Floer Memorial Volume, Birkhäuser 1995.
  26. K. Ono, On the Arnold conjecture for weakly monotone symplectic manifolds, Invent. Math. 119 (1995), 519-537.
  27. S. Piunikhin, D. Salamon and M. Schwarz, Symplectic Floer-Donaldson theory and quantum cohomology, in: Contact and Symplectic Geometry, ed. by C. B. Thomas, Cambridge Univ. Press 1996.
  28. Y. Ruan, Virtual neighborhoods and pseudoholomorphic curves, preprint 1996.
  29. D. Salamon, Morse theory, the Conley index and Floer homology, Bull. London Math. Soc. 22 (1990), 113-140.
  30. D. Salamon and E. Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992), 1303-1360.
  31. M. Schwarz, Quantum cup-length estimate for symplectic fixed points, preprint 1996.
  32. M. Schwarz, Morse homology, Progress in Math. 111, Birkhäuser, 1993.
  33. B. Siebert, Gromov-Witten invariants for general symplectic manifolds, preprint 1996.
Banach Center Publications
1998/45/1
Export to PBN, Opens in new tab
Pages:
13-24
Main language of publication
English
Published
1998
Exact and natural sciences