2026-08-15T10:57:18Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19993 2024-06-06T06:21:15Z ddc:004 open_access

Hopf Arborescent Links, Minor Theory, and Decidability of the Genus Defect Dehornoy, Pierre Lunel, Corentin de Mesmay, Arnaud Knot Theory Genus Slice Genus Hopf Arborescent Links Well-Quasi-Order While the problem of computing the genus of a knot is now fairly well understood, no algorithm is known for its four-dimensional variants, both in the smooth and in the topological locally flat category. In this article, we investigate a class of knots and links called Hopf arborescent links, which are obtained as the boundaries of some iterated plumbings of Hopf bands. We show that for such links, computing the genus defects, which measure how much the four-dimensional genera differ from the classical genus, is decidable. Our proof is non-constructive, and is obtained by proving that Seifert surfaces of Hopf arborescent links under a relation of minors defined by containment of their Seifert surfaces form a well-quasi-order. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Pierre Dehornoy and Corentin Lunel and Arnaud de Mesmay 2024 Is Part Of LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2024.48 urn:nbn:de:0030-drops-199938 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.48 eng https://creativecommons.org/licenses/by/4.0/legalcode