Symplectic Topology: An Introduction

  • Claude Viterbo
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 15)


The aim of this survey is to review progress in symplectic topology during the last 25 years, that is, since 1968. Our task is made a little easier by the fact that symplectic topology was only born around 1983.


Periodic Orbit Symplectic Manifold Lagrange Submanifold Zero Section Holomorphic Curve 
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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  1. [B]
    Bennequin, D., Problèmes elliptiques surfaces de Riemann et structures symplectiques, Séminaire Bourbaki 1985–1986, exposé 657, Astérisque, vol. 138.Google Scholar
  2. [Bi]
    Birkhoff, G., Dynamical Systems, AMS Publications 1924.Google Scholar
  3. [C]
    Chaperon, M., Quelques questions de géométrie symplectique, Séminaire Bourbaki 1982–1983, Astérisque, vol. 105–106, pp. 231–249.Google Scholar
  4. [Co-Z]
    Conley, C. and Zehnder, E., Morse type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math., vol. 37 (1984), pp. 207–253.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [E-H1]
    Ekeland, I. and Hofer, H., Symplectic topology and Hamiltonian dynamics, Math. Zeitschrift, vol. 200 (1989), pp. 355–378.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [E-H2]
    Ekeland, I., Hofer, H., Symplectic topology and Hamiltonian dynamics II, Math. Zeitschrift, vol. 203 (1990), pp. 355–378.MathSciNetCrossRefGoogle Scholar
  7. [G1]
    Gromov, M., Pseudo holomorphic curves on almost complex manifolds, Inventiones Math., vol. 82 (1985), pp. 307–347.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [G2]
    Gromov, M., Soft and Hard Symplectic Geometry, in Proceedings of the International Congress of Mathematicians 1986, vol.1 (1987), pp. 81–98.Google Scholar
  9. [VI]
    Viterbo, C., Capacités symplectiques et applications, Séminaire Bourbaki, juin 89, expose 714, Astérisque, vol. 177–178 (1990).Google Scholar
  10. [V2]
    Viterbo, C., Symplectic topology as the geometry of generating functions, Mathematische Annalen, vol. 692 (1992), pp. 685–710.MathSciNetCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1995

Authors and Affiliations

  • Claude Viterbo
    • 1
  1. 1.Département de Mathématique Bâtiment 425Université de Paris-SudOrsay CedexFrance

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