Geometric automorphism groups of symplectic 4-manifolds

Let M be a closed, oriented, smooth 4-manifold with intersection form Γ, A ( Γ ) the automorphism group of Γ and D ( M ) the subgroup induced by orientation-preserving diffeomorphisms of M. In this note we study the question when D ( M ) is of infinite index in A ( Γ ) for a symplectic 4-manifold.