Quasipositive fiber surfaces are not well-quasi-ordered

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

Publication Details

Journal
ArXiv.org
Published
2025-09-26
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

Quasipositive fiber surfaces are not well-quasi-ordered

ArXiv.org
Geochemistry and Geologic Mapping
article

Quasipositive fiber surfaces are not well-quasi-ordered

article en

Abstract

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

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 25%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
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Quasipositive fiber surfaces are not well-quasi-ordered · ArXiv.org (2025) | TGRS Research Map | TGRS