On a theorem of Chekanov

Emmanuel Ferrand

ArticleOriginal scientific text

Title

On a theorem of Chekanov

Authors ¹

Affiliations

Centre de Mathématiques (U.R.A. 169 du C.N.R.S.), École Polytechnique, 91128 Palaiseau cedex, France

Abstract

A proof of the Chekanov theorem is discussed from a geometric point of view. Similar results in the context of projectivized cotangent bundles are proved. Some applications are given.

[A] V. Arnold, Topological invariants of plane curves and caustics, Univ. Lecture Ser. 5, Amer. Math. Soc., 1994.
[A-V-G] V. Arnold, A. Varchenko, S. Goussein-Zadé, Singularités des applications différentiables, I. Classification des points critiques, des caustiques et des fronts d'ondes, Mir, Moscou, 1986.
[B] M. Brunella, On a theorem of Sikorav, Enseign. Math. 37 (1991), 83-87.
[C] Y. Chekanov, Critical points of quasi-functions and generating families of Legendrian manifolds, Funktsional. Anal. i Prilozhen. 30 (1996).
[Ch] M. Chaperon, On generating families, in: The Floer Memorial Volume, Helmut Hofer ed., Progr. Math. 133, Birkhäuser, 1995.
[Ch-Z] M. Chaperon, E. Zehnder, Quelques résultats globaux en géométrie symplectique, in Géométrie symplectique et de contact: autour du théorème de Poincaré-Birkhoff, P. Dazord, N. Desolneux-Moulis (eds.), Travaux en Cours, Hermann, Paris, 1984, 51-121.
[L-S] F. Lalonde, J. C. Sikorav, Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents, Comment. Math. Helv. 66 (1991), 18-33.
[Si] J. C. Sikorav, Problèmes d'intersections et de points fixes en géométrie Hamiltonienne, Comment. Math. Helv. 62 (1987), 62-73.
[T-W] F. Takens, J. White, Morse theory of double normals of immersions, Indiana Univ. Math. J. 21 (1971), 11-17.
[Th] D. Théret, Ph. D. Thesis, Université Paris VII, to appear.
[V] C. Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992), 685-710.

Title

On a theorem of Chekanov

Affiliations

Abstract

Bibliography