# On sign assignments in link Floer homology

## TL;DR

This paper compares two sign assignment methods in link Floer homology, showing that with minor adjustments, they produce identical chain complexes, thus unifying different approaches in the field.

## Contribution

It demonstrates the equivalence of two sign assignment conventions in link Floer homology through a simple modification, unifying their resulting chain complexes.

## Key findings

- Different sign assignments can be made equivalent with a small modification.
- The two methods produce identical chain complexes after adjustment.
- The comparison clarifies the relationship between combinatorial and orientation-based sign conventions.

## Abstract

In this short note, we compare the combinatorial sign assignment of Manolescu, Ozsvath, Szabo and Thurston for grid homology of knots and links in 3-sphere 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.