We use grid diagrams to give a combinatorial algorithm for computing the knot Floer homology of the pullback of a knot in its –fold cyclic branched cover , and we give computations when for over fifty three-bridge knots with up to eleven crossings.
"Computing knot Floer homology in cyclic branched covers." Algebr. Geom. Topol. 8 (2) 1163 - 1190, 2008. https://doi.org/10.2140/agt.2008.8.1163