The number of Hamiltonian fixed points on symplectically aspherical manifolds

TL;DR

This paper proves that on symplectically aspherical closed manifolds, a generic Hamiltonian diffeomorphism has at least the stable Morse number of fixed points, supporting Arnold's conjecture.

Contribution

It establishes a lower bound on the number of fixed points for generic Hamiltonian diffeomorphisms on symplectically aspherical manifolds, confirming a key aspect of Arnold's conjecture.

Findings

At least the stable Morse number of fixed points for generic Hamiltonian diffeomorphisms

Supports Arnold's conjecture in the symplectically aspherical case

Provides a lower bound consistent with Morse theory principles

Abstract

We show that a generic Hamiltonian diffeomorphism on a closed symplectic manifold which is symplectically aspherical has at least the stable Morse number of fixed points - this is in line with a conjecture by Arnold.