A short proof of cuplength estimates on Lagrangian intersections

Wenmin Gong; Wenmin Gong

doi:10.3934/cam.2023003

Communications in Analysis and Mechanics

2023, Volume 15, Issue 2: 50-57. doi: 10.3934/cam.2023003

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Research article

A short proof of cuplength estimates on Lagrangian intersections

Wenmin Gong ^,

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

Received: 08 December 2022 Revised: 23 February 2023 Accepted: 07 March 2023 Published: 09 March 2023
53D40, 58F05, 58E05

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.
- Arnold's conjecture,
- cuplength estimates,
- Lagrangian intersections,
- spectral invariants
Citation: Wenmin Gong. A short proof of cuplength estimates on Lagrangian intersections[J]. Communications in Analysis and Mechanics, 2023, 15(2): 50-57. doi: 10.3934/cam.2023003

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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.

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