English

Quasipositive fiber surfaces are not well-quasi-ordered

Geometric Topology 2025-09-29 v1 Symplectic Geometry

Abstract

By exhibiting an explicit infinite anti-chain, we show that the class of quasipositive fiber surfaces in S3S^3 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.

Keywords

Cite

@article{arxiv.2509.22608,
  title  = {Quasipositive fiber surfaces are not well-quasi-ordered},
  author = {Joseph Breen and Michele Capovilla-Searle},
  journal= {arXiv preprint arXiv:2509.22608},
  year   = {2025}
}

Comments

16 pages, 9 figures, comments welcome