Closed-open morphisms on periodic Floer homology

TL;DR

This paper constructs and analyzes closed-open morphisms from periodic Floer homology to quantitative Heegaard Floer homology, establishing their non-vanishing and relating spectral invariants.

Contribution

It introduces the concept of closed-open morphisms between PFH and Heegaard Floer homology, providing a cylindrical formulation and proving their non-vanishing.

Findings

Constructed closed-open morphisms under certain Lagrangian link assumptions.

Proved the morphisms are non-vanishing.

Established a relation between PFH and HF spectral invariants.

Abstract

In this note, we investigate homomorphisms from the periodic Floer homology (PFH) to the quantitative Heegaard Floer homology. We call the homomorphisms closed-open morphisms. Under certain assumptions on the Lagrangian link, we first follow R. Lipshitz's idea to give a cylindrical formulation of the quantitative Heegaard Floer homology. Then we construct the closed-open morphisms from the PFH to the quantitative Heegaard Floer homology. Moreover, we show that the morphisms are non-vanishing. As an application, we deduce a relation between the PFH-spectral invariants and the HF-spectral invariants.