On knot Floer homology and cabling

الأصل · EN

This paper is devoted to the study of the knot Floer homology groups HFK(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 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((T₂,₂ₘ₊₁)₂,₂ₙ₊₁) for all sufficiently large |n|, where T₂,₂ₘ₊₁ denotes the (2,2m+1)-torus knot.