## Duke Mathematical Journal

### Transversality in elliptic Morse theory for the symplectic action

#### Article information

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

Dates
First available in Project Euclid: 19 February 2004

http://projecteuclid.org/euclid.dmj/1077245861

Digital Object Identifier
doi:10.1215/S0012-7094-95-08010-7

Mathematical Reviews number (MathSciNet)
MR1360618

Zentralblatt MATH identifier
0846.58025

#### Citation

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.

#### References

• [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).