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Research Article | Open Access

A short proof of cuplength estimates on Lagrangian intersections

School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China
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Abstract

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.

Keywords

Arnold's conjecturecuplength estimatesLagrangian intersectionsspectral invariants
CLC number: 53D40, 58F05, 58E05

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Communications in Analysis and Mechanics
Volume 15 Issue 2,
June 2023
Pages 50-57
DOI: 10.3934/cam.2023003

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Cite this article:
Gong W. A short proof of cuplength estimates on Lagrangian intersections. Communications in Analysis and Mechanics, 2023, 15(2): 50-57. https://doi.org/10.3934/cam.2023003

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Received: 08 December 2022
Revised: 23 February 2023
Accepted: 07 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)