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

Daniele Celoria

Published 2015-10-24Version 1

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 $\widehat{GH} (L(p,q),K;\mathbb{Z})$, and provide empirical evidence supporting the absence of torsion in these groups.