On a theorem of Chekanov

Emmanuel Ferrand

Banach Center Publications (1997)

  • Volume: 39, Issue: 1, page 39-48
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Ferrand, Emmanuel. "On a theorem of Chekanov." Banach Center Publications 39.1 (1997): 39-48. <http://eudml.org/doc/208677>.

@article{Ferrand1997,
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.},
author = {Ferrand, Emmanuel},
journal = {Banach Center Publications},
keywords = {contact structures; Legendrian isotopy; generating family quadratic at infinity; wave front},
language = {eng},
number = {1},
pages = {39-48},
title = {On a theorem of Chekanov},
url = {http://eudml.org/doc/208677},
volume = {39},
year = {1997},
}

TY - JOUR
AU - Ferrand, Emmanuel
TI - On a theorem of Chekanov
JO - Banach Center Publications
PY - 1997
VL - 39
IS - 1
SP - 39
EP - 48
AB - 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.
LA - eng
KW - contact structures; Legendrian isotopy; generating family quadratic at infinity; wave front
UR - http://eudml.org/doc/208677
ER -

References

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  1. [A] V. Arnold, Topological invariants of plane curves and caustics, Univ. Lecture Ser. 5, Amer. Math. Soc., 1994. 
  2. [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. 
  3. [B] M. Brunella, On a theorem of Sikorav, Enseign. Math. 37 (1991), 83-87. Zbl0739.58015
  4. [C] Y. Chekanov, Critical points of quasi-functions and generating families of Legendrian manifolds, Funktsional. Anal. i Prilozhen. 30 (1996). 
  5. [Ch] M. Chaperon, On generating families, in: The Floer Memorial Volume, Helmut Hofer ed., Progr. Math. 133, Birkhäuser, 1995. 
  6. [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. 
  7. [L-S] F. Lalonde, J. C. Sikorav, Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents, Comment. Math. Helv. 66 (1991), 18-33. 
  8. [Si] J. C. Sikorav, Problèmes d'intersections et de points fixes en géométrie Hamiltonienne, Comment. Math. Helv. 62 (1987), 62-73. Zbl0684.58015
  9. [T-W] F. Takens, J. White, Morse theory of double normals of immersions, Indiana Univ. Math. J. 21 (1971), 11-17. Zbl0228.58007
  10. [Th] D. Théret, Ph. D. Thesis, Université Paris VII, to appear. 
  11. [V] C. Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992), 685-710. Zbl0735.58019

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