Papers › L-space satellite operators and knot Floer homology
L-space satellite operators and knot Floer homology
Daren Chen, Ian Zemke, Hugo Zhou
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We consider satellite operators where the corresponding 2-component link is an L-space link. This family includes many commonly studied satellite operators, including cabling operators, the Whitehead operator, and a family of Mazur operators. We give a formula which computes the knot Floer complex of a satellite of K in terms of the knot Floer complex of K. Our main tools are the Heegaard Floer Dehn surgery formulas and their refinements. A key step in our computation is a proof that 2-component L-space links have formal knot Floer complexes. We use this to show that the link Floer complexes of 2-component L-space links are determined by their multivariable Alexander polynomials. We implement our satellite formula in Python code, which we also make available.
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