On knot Floer homology and cabling

Hedden, Matthew¹

¹Department of Mathematics, Princeton University, Princeton NJ 08544-1000, USA

Algebraic and Geometric Topology, Tome 5 (2005) no. 3, pp. 1197-1222

Résumé

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

Détail

DOI : 10.2140/agt.2005.5.1197

Keywords: knots, Floer homology, cable, satellite, Heegaard diagrams

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