Hamiltonian loops on the symplectic one-point blow up

TL;DR

This paper demonstrates how Hamiltonian loops on a symplectic manifold can be lifted to its one-point blow up and uses Weinstein's morphism to show the infinite order of these loops in the fundamental group of Hamiltonian diffeomorphisms.

Contribution

It introduces a method to lift Hamiltonian loops to the symplectic one-point blow up and proves their infinite order using Weinstein's morphism.

Findings

Lifted Hamiltonian loops have infinite order on the fundamental group.

The method applies to symplectic one-point blow ups.

Uses Weinstein's morphism to analyze loop properties.

Abstract

We lift a Hamiltonian loop on a symplectic manifold to a Hamiltonian loop on the symplectic one-point blow up of a symplectic manifold. Then we use Weinstein's morphism to show that the lifted Hamiltonian loop has infinite order on the fundamental group of the group of Hamiltonian diffeomorphisms of the blown up manifold.