Cobordism maps on periodic Floer homology induced by elementary Lefschetz fibrations

Abstract

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.

The previous title of this paper is "An example of cobordism map on PFH". I change it to the current title. The exposition of this paper has been improved. Any comments are welcome

References in corpus (3)

• Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms
• On cobordism maps on periodic Floer homology
• Taming the pseudoholomorphic beasts in $\mathbb{R}\times (S^1\times S^2)$