ribbon concordance与cabling（缆化）
Ribbon concordance and cabling
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中文总结 AI 辅助
本文提出关于 ribbon concordance 与缆化纽结的猜想，证明其在特定情形成立，运用纽结 Floer 同调的最小高度不变量，还得到相关亏格界，为纽结理论研究提供新结论。
中文摘要 AI 辅助
我们研究到缆化纽结的 ribbon concordance（ ribbon 协边）。我们提出一个猜想：任何容许到(p,q)-缆化纽结的 ribbon concordance 的非平凡纽结，其自身必为一个(p,q)-缆化纽结。我们证明了当容许 ribbon concordance 的纽结已是相同伴随的缆化纽结、是环面纽结或亏格为1时，该猜想成立；我们还对一大类目标缆化纽结验证了该猜想。证明使用了从纽结 Floer 同调的浸入曲线表述定义的最小高度不变量，该不变量可阻碍 ribbon concordance，并意味着任何容许到纤维型缆化纽结的 ribbon concordance 的非平凡纽结是素纽结。我们还建立了容许到缆化纽结的 ribbon concordance 的纽结的亏格界。
英文摘要
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.
