  We prove that $\pi_1(\text{Ham}(M))$ 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
$\pi_1(\text{Ham}(M))$ to contain an infinite cyclic subgroup, when $M$ is a
general toric manifold.
