Ribbon Homology Cobordisms and Link Floer Homology

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 ${\mathcal{HF}\mathcal{L}}^{-}$. We also make use of the torsion submodule of ${\text{HFL}}^{-}$ to give restrictions on the number of critical points in ribbon homology concordances.

Minor changes made, thanks to helpful comments of the referee. This version to appear in the Journal of Symplectic Geometry