Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 5, Number 3 (2005), 1197-1222.
On knot Floer homology and cabling
This paper is devoted to the study of the knot Floer homology groups , where denotes the cable of an arbitrary knot, . It is shown that for sufficiently large , the Floer homology of the cabled knot depends only on the filtered chain homotopy type of . A precise formula for this relationship is presented. In fact, the homology groups in the top 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 cables. As an example we compute for all sufficiently large , where denotes the –torus knot.
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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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