Genus-zero links with prescribed knots as components

Raphael Appenzeller; José Pedro Quintanilha

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arXiv · 2607.12729

Genus-zero links with prescribed knots as components

Raphael Appenzeller·José Pedro Quintanilha

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Abstract

We prove that any finite collection of at least three isotopy classes of knots in a 3-manifold $M$ is realizable as the components of a genus-zero link in $M$, provided that an obvious requirement on their conjugacy classes in $\pi_1(M)$ is met. This condition is vacuously satisfied for $M = \mathbb S^3$, and in this case we also control the pairwise linking numbers of the components. Replacing the 3-genus with the 4-genus, we obtain an analogous result where only two knot isotopy classes are prescribed.

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BibTeX RIS

Raphael Appenzeller, José Pedro Quintanilha. 2026-07-14. Genus-zero links with prescribed knots as components. https://arxiv.org/abs/2607.12729

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