On Sign Assignments in Link Floer Homology

Abstract

In this short note, we compare the combinatorial sign assignment of Manolescu, Ozsváth, Szabó, and Thurston for grid homology of knots and links in ${\mathit{S}}^3$ with the sign assignment coming from a coherent system of orientations on Whitney disks. Although these constructions produce different signs, a small modification of the convention in either of the two methods results in identical sign assignments, and thus identical chain complexes.