2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221930Modifying the method of [21], we compute the perturbed $HF^+$ for some special classes of fibered three manifolds in the second highest spin$^c$-structures $S_{g-2}$. The special classes considered in this paper include the mapping tori of Dehn twists along a single non-separating curve and along a transverse pair of curves.11 pages, 7 figuresSymplectic GeometryGeometric Topology57R58text