L-space satellite operators and knot Floer homology

Daren Chen; Ian Zemke; Hugo Zhou

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arXiv · 2412.05755

L-space satellite operators and knot Floer homology

Daren Chen·Ian Zemke·Hugo Zhou

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Abstract

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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BibTeX RIS

Daren Chen, Ian Zemke, Hugo Zhou. 2024-12-07. L-space satellite operators and knot Floer homology. https://arxiv.org/abs/2412.05755

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