  Based on recent work of T. Draghici, T.-J. Li and W. Zhang, we further
investigate properties of the dimension h_J of the J-anti-invariant cohomology
subgroup H_J of a closed almost Hermitian 4-manifold (M, g, J, F) using metric
compatible and symplectic 2-form compatible almost complex structures. We prove
that h_J = 0 for generic almost complex structures J on M.
