On grid homology for lens space links: combinatorial invariance and integral coefficients

TL;DR

This paper proves that grid homology for links in lens spaces is a combinatorial invariant and extends it to integral coefficients, confirming its robustness and invariance properties.

Contribution

It establishes combinatorial invariance of grid homology in lens spaces and extends the theory to integral coefficients using sign assignments.

Findings

Grid homology in lens spaces is a link invariant.

Extension of grid homology to integral coefficients is valid.

The invariance is proven using combinatorial methods and sign assignments.

Abstract

Following the approach to grid homology of links in $S^3$, we prove combinatorially that the grid homology of links in lens spaces defined by Baker, Grigsby, and Hedden is a link invariant. Further, using the sign assignment defined by Celoria, we prove that the generalization of grid homology to integral coefficients is a link invariant.