On Arnold's conjecture for symplectic fixed points

Kaoru Ono

Banach Center Publications (1998)

  • Volume: 45, Issue: 1, page 13-24
  • ISSN: 0137-6934

How to cite

top

Ono, Kaoru. "On Arnold's conjecture for symplectic fixed points." Banach Center Publications 45.1 (1998): 13-24. <http://eudml.org/doc/208899>.

@article{Ono1998,
author = {Ono, Kaoru},
journal = {Banach Center Publications},
keywords = {critical point; fixed point; Morse function; symplectic manifold},
language = {eng},
number = {1},
pages = {13-24},
title = {On Arnold's conjecture for symplectic fixed points},
url = {http://eudml.org/doc/208899},
volume = {45},
year = {1998},
}

TY - JOUR
AU - Ono, Kaoru
TI - On Arnold's conjecture for symplectic fixed points
JO - Banach Center Publications
PY - 1998
VL - 45
IS - 1
SP - 13
EP - 24
LA - eng
KW - critical point; fixed point; Morse function; symplectic manifold
UR - http://eudml.org/doc/208899
ER -

References

top
  1. [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. Zbl0297.58008
  2. [2] V. I. Arnold, Mathematical Methods in Classical Mechanics, Graduate Text in Mathematics 60, Springer Verlag. 
  3. [3] K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. (1997). Zbl0909.14007
  4. [4] M. Chaperon, Une idée du type géodesiques brisées, Comptes Rendues Paris 298 (1984), 293-296. Zbl0576.58010
  5. [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. Zbl0867.58026
  6. [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. [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. [8] A. Floer, Holomorphic spheres and symplectic fixed points, Comm. Math. Phys. 120 (1989), 575-611. Zbl0755.58022
  9. [9] A. Floer and H. Hofer, Coherent orientations for periodic orbits problems in symplectic geometry, Math. Z. 212 (1993), 13-38. Zbl0789.58022
  10. [10] A. Floer, H. Hofer and D. Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. Journ. 80 (1995), 251-292. Zbl0846.58025
  11. [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. Zbl0871.57032
  12. [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. Zbl1004.53063
  13. [13] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. Zbl0592.53025
  14. [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. [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. Zbl0842.58029
  16. [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. Zbl0885.14028
  17. [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. [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. Zbl0592.58023
  19. [19] H. V. Lê and K. Ono, Symplectic fixed points, the Calabi invariant and Novikov homology, Topology 34 (1995), 155-176. Zbl0822.58019
  20. [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. Zbl0874.53030
  21. [21] J. Li and G. Tian, Virtual moduli cycles and Gromov-Witten invariants for general symplectic manifolds, preprint 1996. 
  22. [22] G. Liu and G. Tian, preprint 1996. 
  23. [23] D. McDuff, Elliptic methods in symplectic geometry, Bull. Amer. Math. Soc. 23 (1990), 311-358. Zbl0723.53018
  24. [24] D. McDuff and D. Salamon, J-holomorphic curves and quantum cohomology, University Lecture Ser., 6, Amer. Math. Soc. 1994. Zbl0809.53002
  25. [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. Zbl0795.58019
  26. [26] K. Ono, On the Arnold conjecture for weakly monotone symplectic manifolds, Invent. Math. 119 (1995), 519-537. Zbl0823.53025
  27. [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. Zbl0874.53031
  28. [28] Y. Ruan, Virtual neighborhoods and pseudoholomorphic curves, preprint 1996. 
  29. [29] D. Salamon, Morse theory, the Conley index and Floer homology, Bull. London Math. Soc. 22 (1990), 113-140. Zbl0709.58011
  30. [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. Zbl0766.58023
  31. [31] M. Schwarz, Quantum cup-length estimate for symplectic fixed points, preprint 1996. 
  32. [32] M. Schwarz, Morse homology, Progress in Math. 111, Birkhäuser, 1993. 
  33. [33] B. Siebert, Gromov-Witten invariants for general symplectic manifolds, preprint 1996. 

NotesEmbed ?

top

You must be logged in to post comments.