Quasipositive fiber surfaces are not well-quasi-ordered

2025/09/26 by Breen, Joseph, Capovilla-Searle, Michele
#57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2509.22608

Abstract

By exhibiting an explicit infinite anti-chain, we show that the class of quasipositive fiber surfaces in S³ is not well-quasi-ordered under the surface minor relation. This answers questions raised by Baader-Dehornoy-Liechti and Dehornoy-Lunel-de Mesmay in the negative.

Citations

• Hopf Arborescent Links, Minor Theory, and Decidability of the Genus Defect
• The contact invariant in sutured Floer homology
• Notions of positivity and the Ozsvath-Szabo concordance invariant
• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• A characterization of quasipositive Seifert surfaces (Constructions of quasipositive knots and links, III)

Related

• Minor theory for quasipositive surfaces
• A characterization of quasipositive Seifert surfaces (Constructions of quasipositive knots and links, III)
• Minor theory for surfaces and divides of maximal signature
• Positive links are strongly quasipositive
• Non-fibered strongly quasipositive links and tightness