Combinatorial knot Floer homology and cyclic branched covers

Abstract

Using a Heegaard diagram for the pullback of a knot $K\subset S^3$ in its cyclic branched cover ${\Sigma }_m(K)$ obtained from a grid diagram for $K$, we give a combinatorial proof for the invariance of the associated combinatorial knot Floer homology over $\mathbb{Z}$.