On cobordism maps on periodic Floer homology

Abstract

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.

arXiv commentThe preview title of this paper is "Cobordism Maps on PFH induced by Lefschetz Fibration over Higher Genus Base". According to referees'suggestion, I change it to be "On cobordism maps on periodic Floer homology". In this version, the exposition of the paper is improved. Besides, I correct some mistakes about the composition rule and restate Theorem 1 for a general setting

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Cited by in corpus (5)

• Proof of the simplicity conjecture
• PFH spectral invariants and $C^{\infty }$ closing lemmas
• Product and Coproduct on Fixed Point Floer Homology of Positive Dehn Twists
• Closed-open morphisms on periodic Floer homology
• Cobordism maps on periodic Floer homology induced by elementary Lefschetz fibrations