Volume 5, issue 3 (2005)

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On knot Floer homology and cabling

Matthew Hedden

Algebraic & Geometric Topology 5 (2005) 1197–1222

arXiv: math.GT/0406402


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.

knots, Floer homology, cable, satellite, Heegaard diagrams
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57R58
Forward citations
Received: 9 August 2004
Revised: 23 July 2005
Accepted: 14 March 2005
Published: 20 September 2005
Matthew Hedden
Department of Mathematics
Princeton University
Princeton NJ 08544-1000