This paper is devoted to the study of the knot Floer homology groups HFK(S^3,K_{ 2,n}), where K_{ 2,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 CFK(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 HFK((T_{ 2,2m+1})_{ 2,2n+1}) for all sufficiently large |n|, where T_{ 2,2m+1} denotes the (2,2m+1)-torus knot.
Categories: math.GT math.SG