  We construct a local characteristic map to a symplectic manifold M via
certain cohomology groups of Hamiltonian vector fields. For each p in M, the
Leibniz cohomology of the Hamiltonian vector fields on R^{2n} maps to the
Leibniz cohomology of all Hamiltonian vector fields on M. For a particular
extension g_n of the symplectic Lie algebra, the Leibniz cohomology of g_n is
shown to be an exterior algebra on the canonical symplectic two-form. The
Leibniz homology of g_n then maps to the Leibniz homology of Hamiltonian vector
fields on R^{2n}.
