The action-Maslov homomorphism I : pi1(Ham(X, o)) → 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 D (a generalization of having homology generated by divisor classes). These properties hold for products of projective spaces, the Grassmannian of 2 planes in C4 , and tonic 4-manifolds. We show that these properties do not hold for all Grassmannians. Finally, the relationship between these statements and the geometry of pi1(Ham(X, o)) is explored.
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