  In this article, we investigate the cobordism maps on periodic Floer homology
(PFH). In the first part of the paper, we define the cobordism maps on PFH via
Seiberg Witten theory as well as the isomorphism between PFH and Seiberg Witten
cohomology. Furthermore, we show that the maps satisfy the holomorphic curve
axiom. In the second part of the paper, we give an alternative definition of
these maps by using holomorphic curve method, provided that the symplectic
cobordisms are Lefschetz fibration satisfying certain nice conditions. Under
additionally certain monotonicity assumptions, we show that these two
definitions are equivalent.
