Algebraic & Geometric Topology

On knot Floer homology and cabling

Matthew Hedden

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796449

Digital Object Identifier
doi:10.2140/agt.2005.5.1197

Mathematical Reviews number (MathSciNet)
MR2171808

Zentralblatt MATH identifier
1086.57014

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

Keywords
knots Floer homology cable satellite Heegaard diagrams

Citation

Hedden, Matthew. On knot Floer homology and cabling. Algebr. Geom. Topol. 5 (2005), no. 3, 1197--1222. doi:10.2140/agt.2005.5.1197. https://projecteuclid.org/euclid.agt/1513796449


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