Ribbon concordance and cabling

Jennifer Hom; JungHwan Park

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arXiv · 2608.06625

Ribbon concordance and cabling

Jennifer Hom·JungHwan Park

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Abstract

We study ribbon concordances to cable knots. We formulate a conjecture predicting that any nontrivial knot admitting a ribbon concordance to a (p,q)-cable must itself be a (p,q)-cable. We prove the conjecture when the knot admitting the ribbon concordance is already a cable of the same companion, is a torus knot, or has genus one. We also verify it for a broad class of target cables. The proofs use a minimum-height invariant defined from the immersed-curve formulation of knot Floer homology. This invariant obstructs ribbon concordances and implies that any nontrivial knot admitting a ribbon concordance to a fibered cable knot is prime. We also establish genus bounds for knots admitting ribbon concordances to cable knots.

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BibTeX RIS

Jennifer Hom, JungHwan Park. 2026-08-06. Ribbon concordance and cabling. https://arxiv.org/abs/2608.06625

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