On knot Floer homology and cabling

Abstract This paper is devoted to the study of the knot Floer homology groups ĤFK(S3,K2,n), where K2,n denotes the (2, n) cable of an arbitrary knot, K. It is shown that for sufficiently large |n|, the Floer homology of the cabled knot depends only on the filtered chain homotopy type of ĈFK(K). A precise formula for this relationship is presented. In fact, the homology groups in the top 2 filtration dimensions for the cabled knot are isomorphic to the original knot’s Floer homology group in the top filtration dimension. The results are extended to (p, pn ± 1) cables. As an example we compute ĤFK((T2,2m+1)2,2n+1) for all sufficiently large |n|, where T2,2m+1 denotes the (2, 2m+ 1)-torus knot. AMS Classification 57M27; 57R5