Hamiltonian loops on the symplectic blow up along a submanifold

TL;DR

This paper demonstrates that the fundamental group of Hamiltonian diffeomorphisms on a symplectic blow-up manifold contains an element of infinite order, using Weinstein's morphism and explicit loop construction.

Contribution

It introduces a novel method to identify infinite order elements in the fundamental group of Hamiltonian diffeomorphisms on blown-up symplectic manifolds.

Findings

The fundamental group contains an element of infinite order.

Explicit construction of Hamiltonian loops with infinite order.

Application of Weinstein's morphism to the blow-up setting.

Abstract

We prove that the fundamental group of the group of Hamiltonian diffeomorphisms of the symplectic manifold that is obtain by blowing up a submanifold contains an element of infinite order. We prove this using Weinstein's morphism and by constructing explicitly such loop of Hamiltonian diffeomorphisms.