Meridian-link characterization of ribbon minimal knots

Let KK be a knot in S3S^3, and let μK\mu_K be a meridian of KK. Define the two-component link

LK=KμK.L_K=K\sqcup\mu_K.

A link is ribbon concordance minimal if it has no strictly smaller link under ribbon concordance, and a knot is ribbon minimal if it has no strictly smaller knot under ribbon concordance. Meridian-link conjecture. The link LKL_K is ribbon concordance minimal if and only if KK is ribbon minimal. The authors state that this conjecture is unproved and expect a general resolution to have applications to the study of minimality of satellite knots.

Sources & referencesView supporting material

Primary source

Gary Dunkerley, “A ribbon partial order for links and minimality detection via Heegaard Floer”, arXiv:2606.20802 (2026).

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