Inventiones mathematicae

, Volume 119, Issue 1, pp 519–537 | Cite as

On the Arnold conjecture for weakly monotone symplectic manifolds

  • Kaoru Ono


We show the Arnold conjecture concerning symplectic fixed points in the case that the symplectic manifold is weakly-monotone and all the fixed points are non-degenerate. In particular, the conjecture is true in dimension 2, 4, 6 if all the fixed points are non-degenerate.


Manifold Symplectic Manifold Weakly Monotone Arnold Conjecture Monotone Symplectic Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [A] N. Aronszajin: A unique continuation theorem for solutions for elliptic partial differential equations or inequalities of the second order. J. Math. Appl.36, 235–249 (1957)Google Scholar
  2. [C-Z] C.C. Conley, E. Zehnder: The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold. Invent. Math.73, 33–49 (1983)Google Scholar
  3. [F] A. Floer: Symplectic fixed points and holomorphic spheres. Comm. Math. Phys.120, 575–611 (1989)Google Scholar
  4. A. Floer, H. Hofer: Symplectic homology I (preprint)Google Scholar
  5. [G] M. Gromov: Pseudo holomorphic curves in symplectic manifolds. Invent. Math.82, 307–347 (1985)Google Scholar
  6. H. Hofer, D.A. Salamon: Floer homology and Novikov rings (preprint)Google Scholar
  7. J. Jost: Two-Dimensional Geometric Variational Problems. John Wiley & Sons. 1991Google Scholar
  8. [MD-1] D. McDuff: Examples of symplectic manifolds. Invent. Math.89, 13–36 (1987)Google Scholar
  9. [MD-2] D. McDuff: Symplectic manifolds with contact type boundaries. Invent. Math.103, 651–671 (1991)Google Scholar
  10. D. McDuff, D. Salamon: “Chapter 11 Compactness” (preprint) in a book in preparationGoogle Scholar
  11. [P-W] T.H. Parker, J.G. Wolfson: Pseudo-holomorphic maps and bubble trees, J. Geom. Anal.3, 63–98 (1993)Google Scholar
  12. [Sa] D. Salamon: Morse theory, the Conley index and Floer homology. Bull London Math. Soc.22, 113–140 (1990)Google Scholar
  13. [Sm] S. Smale: An infinite dimensional version of Sard's theorem. Am. J. Math.87, 213–221 (1965)Google Scholar
  14. [S-Z] D. Salamon, E. Zehnder: Morse theory for periodic solutions of Hamiltonian systems and the Maslov index. Comm. Pure. Appl. Math.XLV, 1303–1360 (1992)Google Scholar
  15. R. Ye: Gromov's compactness theorem for pseudo holomorphic curves (preprint)Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Kaoru Ono
    • 1
  1. 1.Max-Planck-Institut für MathematikBonnGermany

Personalised recommendations