## Algebraic & Geometric Topology

### On knot Floer homology and cabling

Matthew Hedden

#### 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

#### 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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