  The action--Maslov homomorphism $I\co\pi_1(\text{Ham}(X,\omega))\to\R$ is an
important tool for understanding the topology of the Hamiltonian group of
monotone symplectic manifolds. We explore conditions for the vanishing of this
homomorphism, and show that it is identically zero when the Seidel element has
finite order and the homology satisfies property $\mathcal{D}$ (a
generalization of having homology generated by divisor classes). We use these
results to show that $I=0$ for products of projective spaces and the
Grassmannian of $2$ planes in $\C^4$.
