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L-space satellite operators and knot Floer homology

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arxiv 2412.05755 v1 pith:WTDWAFU4 submitted 2024-12-07 math.GT

Daren Chen , Ian Zemke , Hugo Zhou This is my paper · ORCID
classification math.GT
keywords floeroperatorssatelliteknotl-spacecomponentlinkcomplex
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Colored knot Floer homology: structures and examples

    math.GT 2025-08 conditional novelty 7.0 of 10

    The authors construct an n-colored knot Floer homology as a colimit over cable links with increasing full twists and equip it with a module structure over an explicit algebra.

  2. The link surgery formula and equivariant surgeries

    math.GT 2025-07 conditional novelty 7.0 of 10

    An equivariant link surgery formula is proved, giving diffeomorphism-induced maps on Heegaard Floer homology, and used to show the kernel of the forgetful map from the equivariant homology cobordism group contains a Z...

  3. Koszul duality and the link surgery formula

    math.GT 2025-07 conditional novelty 7.0 of 10

    The paper defines the curved dg-algebra K!, the Koszul dual of Zemke's surgery algebra K, and proves an equivalence between categories of bonsai, regularly U-adic modules over K and cobonsai, regularly U-adic type-D m...

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