Algebraic & Geometric Topology 5 (2005) 1197–1222

DOI: 10.2140/agt.2005.5.1197

arXiv: math.GT/0406402

Abstract

This paper is devoted to the study of the knot Floer homology groups ^HFK(S³,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.

Keywords

knots, Floer homology, cable, satellite, Heegaard diagrams

Mathematical Subject Classification

Primary: 57M27

Secondary: 57R58

References

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Publication

Received: 9 August 2004
Revised: 23 July 2005
Accepted: 14 March 2005
Published: 20 September 2005

Authors