A short proof of cuplength estimates on Lagrangian intersections

Author:

Gong Wenmin

Abstract

<abstract><p>In this note we give a short proof of Arnold's conjecture for the zero section of a cotangent bundle of a closed manifold. The proof is based on some basic properties of Lagrangian spectral invariants from Floer theory.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference19 articles.

1. V.I. Arnold, Sur une propriété topologique des applications canoniques de la mécanique classique, C. R. Acad. Sci. Paris, 261 (1965), 3719–3722.

2. M. Chaperon, Quelques questions de géométrie symplectique, Séminaire Bourbaki, Astérisque, 1982/83 (1983), 231–249.

3. K.C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problem, Progress in Nonlinear Differential Equations and their Applications, volume 6, Birkhäuser, Boston, MA, 1993. https://doi.org/10.1007/978-1-4612-0385-8

4. C.C. Conley, E. Zehnder, The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold, Invent. Math., 73 (1983), 33–49. https://doi.org/10.1007/BF01393824

5. O. Cornea, G. Lupton, J. Oprea, D. Tanré, Lusternik-Schnirelmann category, volume 103 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2003. https://doi.org/10.1007/978-1-4612-0385-8

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