Gromov invariants of S2-bundles over 4-manifolds

We study the Gromov invariants of the total space W of a symplectic fibration π :W→M, where (M,ω) is a symplectic 4-manifold and the fiber is equal to S2. We find a relation between the Gromov invariants of W and those of M, for the homology classes  such that π(Â)≠0. As an application we construct infinitely many symplectic structures on W for M=E(n), the simply connected minimal elliptic surface.