A ribbon partial order for links and minimality detection via Heegaard Floer

Abstract: We prove that strong ribbon concordance induces a partial order on links in the 3-sphere, extending a theorem of Agol. Using results from knot Floer homology, we certify minimality under the ribbon partial order for a handful of knots and give the first examples of ribbon minimal knots that are not transfinitely nilpotent, resolving a question of Tagami. Using a mixture of classical techniques and recent Heegaard Floer detection results for links, we give several infinite families of links whose members are minimal under the partial order induced by strong ribbon concordance.