Ribbon Homology Cobordisms and Link Floer Homology

TL;DR

This paper explores how link Floer homology behaves under ribbon homology cobordisms, revealing that ribbon homology concordances induce split injections and impose restrictions on critical points, advancing understanding of link invariants in 4D topology.

Contribution

It demonstrates that ribbon homology concordances induce split injections on link Floer homology and provides new restrictions based on torsion submodules, extending prior results.

Findings

Ribbon homology concordances induce split injections on HFL^-

Restrictions on the number of critical points in ribbon homology concordances

Use of torsion submodule to derive new constraints

Abstract

We make use of link Floer homology to study cobordisms between links embedded in 4-dimensional ribbon homology cobordisms. Combining results of Daemi--Lidman--Vela-Vick--Wong and Zemke, we show that ribbon homology concordances induce split injections on $\mathcal{HFL}^-$. We also make use of the torsion submodule of $\text{HFL}^-$ to give restrictions on the number of critical points in ribbon homology concordances.