On knot Floer homology and cabling
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Publication:2571381
DOI10.2140/AGT.2005.5.1197zbMATH Open1086.57014arXivmath/0406402OpenAlexW3105955047MaRDI QIDQ2571381
Author name not available (Why is that?)
Publication date: 1 November 2005
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/math/0406402
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