Closed-open morphisms on periodic Floer homology
Symplectic Geometry
2025-04-08 v5
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.
Keywords
Cite
@article{arxiv.2111.11891,
title = {Closed-open morphisms on periodic Floer homology},
author = {Guanheng Chen},
journal= {arXiv preprint arXiv:2111.11891},
year = {2025}
}
Comments
Improve the exposition. Update Theorem 1. Add an appendix on Seiberg-Witten theory. Comments are welcome!