U-action on perturbed Heegaard Floer homology

This paper has two purposes. First, as a continuation of "Perturbed Floer homology of some fibered three manifolds," we apply a similar method to compute the perturbed HF^+ for some special classes of fibered three-manifolds in the second highest spin^c_- structures, including the mapping tori of Dehn twists along a single non-separating curve and along a transverse pair of curves. Second, we establish an adjunction inequality for the perturbed Heegaard Floer homology, which indicates a potential connection between the U-action on the homology group and the Thurston norm of a three-manifold. As an application, we find the U-action on the perturbed HF^+ of the above classes of fibered three-manifolds is trivial