In this paper, we introduce a sequence of invariants of a knot in : the knot Floer homology groups of the preimage of in the –fold cyclic branched cover over . We exhibit as the categorification of a well-defined multiple of the Turaev torsion of in the case where is a rational homology sphere. In addition, when is a two-bridge knot, we prove that for the spin Spin structure on . We conclude with a calculation involving two knots with identical for which differ as –graded groups.
"Knot Floer homology in cyclic branched covers." Algebr. Geom. Topol. 6 (3) 1355 - 1398, 2006. https://doi.org/10.2140/agt.2006.6.1355