Non-fibered strongly quasipositive links and tightness

Isacco Nonino; Miguel Orbegozo Rodriguez

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arXiv · 2509.26183

Non-fibered strongly quasipositive links and tightness

Isacco Nonino·Miguel Orbegozo Rodriguez

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Abstract

It is well known that for fibered links in $\mathbb{S}^3$ being strongly quasipositive and supporting a tight contact structure are equivalent notions (arXiv:math/0509499). In this note we analyze the relation between these two properties for non fibered links. A non fibered link (together with an incompressible Seifert surface) induces a natural partial open book (arXiv:2509.09615). We prove that strongly quasipositive links induce tight contact structures. We also show that, in contrast to the fibered case, the converse is not true, giving examples of links that are not strongly quasipositive but support tight contact structures.

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Isacco Nonino, Miguel Orbegozo Rodriguez. 2025-09-30. Non-fibered strongly quasipositive links and tightness. https://arxiv.org/abs/2509.26183

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