The Arnold conjecture in $\mathbb C\mathbb P^n$ and the Conley index

TL;DR

This paper provides a new proof of the Arnold conjecture for complex projective space using Conley index theory, confirming the minimum number of fixed points for Hamiltonian diffeomorphisms.

Contribution

It introduces a purely Conley index based proof of the Arnold conjecture in complex projective space, offering an alternative to existing methods.

Findings

Proves the Arnold conjecture in $ ext{CP}^n$ using Conley index

Establishes at least $n+1$ fixed points for Hamiltonian diffeomorphisms

Provides a new topological approach to symplectic fixed point problems

Abstract

In this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in $\mathbb C\mathbb P^n$ asserting that a Hamiltonian diffeomorphism of $\mathbb C\mathbb P^n$ endowed with the Fubini-Study metric has at least $n+1$ fixed points.