Duke Mathematical Journal

Transversality in elliptic Morse theory for the symplectic action

Andreas Floer, Helmut Hofer, and Dietmar Salamon

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J. Volume 80, Number 1 (1995), 251-292.

First available in Project Euclid: 19 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Secondary: 57R70: Critical points and critical submanifolds 58F05


Floer, Andreas; Hofer, Helmut; Salamon, Dietmar. Transversality in elliptic Morse theory for the symplectic action. Duke Math. J. 80 (1995), no. 1, 251--292. doi:10.1215/S0012-7094-95-08010-7. http://projecteuclid.org/euclid.dmj/1077245861.

Export citation


  • [1] C. C. Conley and E. Zehnder, The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold, Invent. Math. 73 (1983), no. 1, 33–49.
  • [2] S. Dostoglou and D. Salamon, Instanton homology and symplectic fixed points, Symplectic geometry ed. D. Salamon, London Math. Soc. Lecture Note Ser., vol. 192, Cambridge Univ. Press, Cambridge, 1993, pp. 57–93.
  • [3] S. Dostoglou and D. A. Salamon, Cauchy-Riemann operators, self-duality, and the spectral flow, to appear in Proceedings of the ECM, Paris, 1992.
  • [4] S. Dostoglou and D. A. Salamon, Self-dual instantons and holomorphic curves, Ann. of Math. (2) 139 (1994), no. 3, 581–640.
  • [5] A. Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988), no. 3, 513–547.
  • [6] A. Floer, Witten's complex and infinite-dimensional Morse theory, J. Differential Geom. 30 (1989), no. 1, 207–221.
  • [7] A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), no. 4, 575–611.
  • [8] A. Floer and H. Hofer, Coherent orientations for periodic orbit problems in symplectic geometry, Math. Z. 212 (1993), no. 1, 13–38.
  • [9] A. Floer and H. Hofer, Symplectic homology. I. Open sets in $\bf C\sp n$, Math. Z. 215 (1994), no. 1, 37–88.
  • [10] H. Hofer and D. A. Salamon, Floer homology and Novikov rings, to appear in Gauge Theory, Symplectic Geometry, and Topology: Essays in Memory of Andreas Floer, ed. by H. Hofer and C. Taubes and A. Weinstein and E. Zehnder, Birkhäuser, 1994.
  • [11] LeHong V., V. Lehong, and K. Ono, Symplectic fixed points, the Calabi invariant and Novikov homology, to appear in Topology.
  • [12] D. McDuff, The local behaviour of holomorphic curves in almost complex $4$-manifolds, J. Differential Geom. 34 (1991), no. 1, 143–164.
  • [13] D. McDuff and D. Salamon, $J$-holomorphic curves and quantum cohomology, University Lecture Series, vol. 6, American Mathematical Society, Providence, RI, 1994.
  • [14] S. P. Novikov, Multivalued functions and functionals–an analogue of the Morse theory, Soviet Math. Dokl. 24 (1981), 222–225.
  • [15] K. Ono, The Arnold conjecture for weakly monotone symplectic manifolds, preprint, 1993.
  • [16] M. Pozniak, Floer homology, Novikov rings and clean intersections, Ph.D. thesis, University of Warwick, 1994.
  • [17] J. Robbin and D. Salamon, The Maslov index for paths, Topology 32 (1993), no. 4, 827–844.
  • [18] J. W. Robbin and D. A. Salamon, The spectral flow and the Maslov index, to appear in Bull. London Math. Soc.
  • [19] D. Salamon, Morse theory, the Conley index and Floer homology, Bull. London Math. Soc. 22 (1990), no. 2, 113–140.
  • [20] D. Salamon and E. Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992), no. 10, 1303–1360.
  • [21] M. Schwarz, Morse homology, Progress in Mathematics, vol. 111, Birkhäuser Verlag, Basel, 1993.
  • [22] S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1973), 213–221.
  • [23] C. Taubes, Personal communication.
  • [24] I. N. Vekua, Generalized analytic functions, Pergamon Press, New York, 1962, trans. and ed. by I. Sneddon.
  • [25] E. Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982), no. 4, 661–692 (1983).