2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75450We prove that $π_1(\text{Ham}(M))$ contains an infinite cyclic subgroup, where $\text{Ham}(M)$ is the Hamiltonian group of the one point blow up of ${\Bbb C}P^3$. We give a sufficient condition for the group $π_1(\text{Ham}(M))$ to contain an infinite cyclic subgroup, when $M$ is a general toric manifold.9 pagesSymplectic GeometryDifferential Geometry53D05; 57S05text