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
Email: mhedden@math.princeton.edu
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