2024/12/07 by Da‐Ren Chen, Chen, Daren, Ian Zemke +3 · 1 citation
Computer Science · Engineering · Mathematics · #57K10 #57K14 #57K18 #Advanced Materials and Mechanics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2412.05755
openalex publication_date 2024/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.