A short proof of cuplength estimates on Lagrangian intersections

TL;DR

This paper provides a concise proof of Arnold's conjecture concerning Lagrangian intersections on cotangent bundles, utilizing properties of Floer spectral invariants.

Contribution

It introduces a simplified proof of a classical conjecture by leveraging fundamental Floer theory properties.

Findings

Proof confirms Arnold's conjecture for cotangent bundles

Utilizes Floer spectral invariants to establish intersection results

Simplifies previous complex proofs

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.