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Mathematische Zeitschrift

, Volume 215, Issue 1, pp 37–88 | Cite as

Symplectic homology I open sets in ℂ n

  • A. Floer
  • H. Hofer
Article

Keywords

Symplectic Manifold Asymptotic Operator Floer Homology Linear Hamiltonian System Exact Triangle 
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.

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References

  1. 1.
    Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. Siam Rev.,18, 620–709 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Amann, H., Zehnder, E.: Periodic solutions of asymptotically linear Hamiltonian systems. Manus Math.,32, 149–189 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Arnold, V.I.: Sur une propriété topologique des applications globalement canoniques de la méchanique classique. C.R. Acad. Sci. Paris,261, 3719–3722 (1965)MathSciNetGoogle Scholar
  4. 4.
    Arnold, V.I.: Mathematical methods of classical mechanics. Chapter Appendix 9. Berlin Heidelberg New York: Springer 1978Google Scholar
  5. 5.
    Benci, V.: Lecture MSRI, Berkeley September 1988Google Scholar
  6. 6.
    Cieliebak, K.: Pseudoholomorphic curves and periodic orbits of Hamiltonian systems on cotangent bundles. Ruhr Universität Bochum, Preprint (1992)Google Scholar
  7. 7.
    Conley, C., Zehnder, E.: The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold. Invent. Math.,73, 33–49 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Conley, C., Zehnder, E.: Morse type index theory for flows and periodic solutions of Hamiltonian equations. Comm. Pure Appl. Math.,37, 207–253 (1984)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Ekeland, I., Hofer, H.: Convex Hamiltonian energy surfaces and their closed trajectories. Commun. Math. Phys.,113, 419–467 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Ekeland, I., Hofer, H.: Symplectic topology and Hamiltonian dynamics. Math. Z.,200, 355–378 (1990)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Ekeland, I., Hofer, H.: Symplectic topology and Hamiltonian dynamics II. Math. Z.,203, 553–567 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Eliashberg, Y., Hofer H.: Towards the definition of symplectic boundary. GAFA,2, 211–220 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Eliashberg, Y., Hofer, H.: Unseen symplectic boundaries PreprintGoogle Scholar
  14. 14.
    Eliashberg, Y., Hofer, H.: An energy capacity inequality for the symplectic holonomy of hypersurfaces flat at infinity. Proc. of a workshop on symplectic geometry, Warwick 1990 (to appear)Google Scholar
  15. 15.
    Floer, A.: A relative index for the symplectic action. Comm. Pure Appl. Math.,41, 393–407 (1988)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Floer, A.: Morse theory for Lagrangian intersection theory. J. Differ. Geom.18, 513–517 (1988)MathSciNetGoogle Scholar
  17. 17.
    Floer, A.: The unregularised gradient flow of the symplectic action. Comm. Pure Appl. Math.41, 775–813 (1988)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Floer, A.: Cuplength estimates on Lagrangian intersections. Comm. Pure Appl. Math.,42, 335–356 (1989)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Floer, A.: Symplectic fixed points and holomorphic spheres. Commun. Math. Phys.,120, 576–611 (1989)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Floer, A.: Witten's complex and infinite dimensional Morse theory. J. Differ. Geom.,30, 207–221 (1989)zbMATHMathSciNetGoogle Scholar
  21. 21.
    Floer, A., Hofer, H.: Coherent orientations for periodic orbit problems in symplectic geometry. Math. Z. (to appear)Google Scholar
  22. 22.
    Floer, A., Hofer, H., Symplectic homology II: General symplectic manifolds (In preparation)Google Scholar
  23. 23.
    Floer, A., Hofer, H., Salamon, D.: A note on unique continuation in the elliptic Morse theory for the action functional. (In preparation)Google Scholar
  24. 24.
    Floer, A., Hofer, H., Wysocki, K.: Applications of symplectic homology I. (Preprint)Google Scholar
  25. 25.
    Floer, A., Hofer, H., Wyasocki, K.: Applications of symplectic homology II. (In preparation)Google Scholar
  26. 26.
    Gromov, M.: Pseuodoholomorphic curves in symplectic manifolds. Inv. Math.,82, 307–347 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Gromov, M.: Soft and hard differential geometry. In: Proceedings of the ICM at Berkeley 1986. pp. 81–89 (1987)Google Scholar
  28. 28.
    Hofer, H.: Ljusternik-Schnirelmann theory for Lagrangian intersections. Ann. Inst. Henri Poincaré,5 (5), 465–499 (1988)zbMATHMathSciNetGoogle Scholar
  29. 29.
    Hofer, H.: On the topological properties of symplectic maps. Proc. R. Soc. Edinburgh115A, 25–38 (1990)MathSciNetGoogle Scholar
  30. 30.
    Hofer, H., Viterbo, C.: The Weinstein conjecture in the presence of holomorphic spheres. Comm. Pure Appl. Math.,45(5), 583–622 (1992)zbMATHMathSciNetGoogle Scholar
  31. 31.
    Hofer, H., Zehnder, E.: Hamiltonian dynamics and symplectic invariants. (In preparation)Google Scholar
  32. 32.
    Hofer, H., Zehnder, E.: Analysis et cetera. Chapter: A new capacity for symplectic manifolds Rabinowitz, P., Zehnder, E. (eds.), pp. 405–428, New York: Academic Press 1990.Google Scholar
  33. 33.
    Lockhard, R., McOwen, R.: Elliptic operators on non compact manifolds. Ann. Sc. Norm. Sup. Pisa12 (12), 409–446 (1985)Google Scholar
  34. 34.
    McDuff, D.: Elliptic methods in symplectic geometry. Bull. AMS23(2), 311–358 (1990)zbMATHMathSciNetGoogle Scholar
  35. 35.
    Rabinowitz, P.: Periodic solutions of Hamiltonian systems. Comm. Pure Appl. Math.31, 157–184 (1978)MathSciNetGoogle Scholar
  36. 36.
    Rabinowitz, P.: Periodic solutions of Hamiltonian systems on a prescribed energy surface. J. Differ. Eq.33, 336–352 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Sachs, J., Uhlenbeck, K.K.: The existence of minimal 2-spheres. Ann. Math.113, 1–24 (1983)CrossRefGoogle Scholar
  38. 38.
    Salamon, D.: Morse theory, the Conley index and Floer homology. Bull. L.M.S. 22, 113–140 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  39. 39.
    Salamon, D., Zehnder, E.: Morse theory for periodic solutions of Hamiltonian systems and the Maslov index. Comm. Pure Appl. Math. (to appear)Google Scholar
  40. 40.
    Salamon, D., Zehnder, E.: Analysis et cetera. Chapter: Floer homology, the Maslov index and periodic orbits of Hamiltonian equations, Rabinowitz, P., Zehnder, E. (eds.), pp., 573–600. New York: Adademic Press 1990Google Scholar
  41. 41.
    Sikorav, J.-C.: Rigidité symplectique dans le cotangent dert n, Duke Math. J.59, 227–231 (1989)CrossRefMathSciNetGoogle Scholar
  42. 42.
    Viterbo, C.: A proof of the Weinstein conjecture in ℝ2n. Ann. Inst. Henri Poncaré, Analyse nonlinéaire4, 337–357 (1987)zbMATHMathSciNetGoogle Scholar
  43. 43.
    Viterbo, C.: Capacités symplectiques et applications. Artéristique, 695 (1989) Séminaire BourbakiGoogle Scholar
  44. 44.
    Viterbo, C.: Symplectic topology as the geometry of generating functions. Math. Ann.292, 685–710 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  45. 45.
    Witten, E.: Supersymmetry and Morse theory, J. Differ. Geom.17, 661–692 (1982)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • A. Floer
    • 1
  • H. Hofer
    • 2
  1. 1.Ruhr-Universität BochumBochumGermany
  2. 2.ETH Zentrum, MathematikZürichSwitzerland

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