Algebraic & Geometric Topology

On knot Floer homology and cabling

Matthew Hedden

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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.

Article information

Algebr. Geom. Topol., Volume 5, Number 3 (2005), 1197-1222.

Received: 9 August 2004
Revised: 23 July 2005
Accepted: 14 March 2005
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57R58: Floer homology

knots Floer homology cable satellite Heegaard diagrams


Hedden, Matthew. On knot Floer homology and cabling. Algebr. Geom. Topol. 5 (2005), no. 3, 1197--1222. doi:10.2140/agt.2005.5.1197.

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