A note on Grid Homology in lens spaces: $\mathbb{Z}$ coefficients and computations

Abstract

We present a combinatorial proof for the existence of the sign refined grid homology in lens spaces, and a self contained proof that ${\partial }_{\mathbb{Z}}^2=0$. We also present a Sage program that computes $\widehat{\mathrm{GH}}(L(p,q),K;\mathbb{Z})$, and provide empirical evidence supporting the absence of torsion in these groups.

25 pages, 23 figures. This version accepted by Glasgow Mathematical Journal

References in corpus (3)

• Lens space surgeries and L-space homology spheres
• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Effective computation of knot Floer homology