Count of genus zero J-holomorphic curves in dimensions four and six

An application of Gromov-Witten invariants is that they distinguish the deformation types of symplectic structures on a smooth manifold. In this manuscript, it is proven that the use of Gromov-Witten invariants in the class of embedded J-holomorphic spheres is restricted. This restriction is in the sense that they cannot distinguish the deformation types of symplectic structures on X-1 x S-2 and X-2 x S-2 for two minimal, simply connected, symplectic 4-manifolds X-1 and X-2 with b(2)(+) (X-1) > 1 and b(2)(+) (X-2) > 1. The result employs the adjunction inequality for symplectic 4-manifolds which is derived from Seiberg-Witten theory.