Algebraic and Geometric Topology 5 (2005), paper no. 48, pages 1197-1222.

On knot Floer homology and cabling

Matthew Hedden

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.

Keywords. Knots, Floer homology, cable, satellite, Heegaard diagrams

AMS subject classification. Primary: 57M27. Secondary: 57R58.

E-print: arXiv:math.GT/0406402

DOI: 10.2140/agt.2005.5.1197

Submitted: 9 August 2004. (Revised: 23 July 2005.) Accepted: 14 March 2005. Published: 20 September 2005.

Notes on file formats

Matthew Hedden
Department of Mathematics, Princeton University
Princeton, NJ 08544-1000, USA

AGT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to