  Periodic Floer homology (PFH) is a Gromov-Floer type invariant for fibered
three-manifolds with Hamiltonian structures. The cobordism maps on periodic
Floer homology induced by symplectic cobordisms are currently only defined
indirectly by using Seiberg-Witten theory. In this paper, we investigate the
cobordism maps induced by a class of symplectic cobordisms constructed by P.
Seidel, called elementary Lefschetz brations. We define the PFH cobordism maps
induced by elementary Lefschetz fibrations in terms of holomorphic curves.
Moreover, we compute these maps for some cases.
