Computing knot Floer homology in cyclic branched covers

Abstract

We use grid diagrams to give a combinatorial algorithm for computing the knot Floer homology of the pullback of a knot $K\subset S^3$ in its $m$–fold cyclic branched cover ${\Sigma }_m\left(K\right)$, and we give computations when $m=2$ for over fifty three-bridge knots with up to eleven crossings.