On transverse-universality of twist knots

Sebastian Zapata

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arXiv · 2402.12585

On transverse-universality of twist knots

Sebastian Zapata

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Abstract

In the search for transverse-universal knots in the standard contact structure on $\mathbb{S}^3$, we present a classification of the transverse twist knots with maximal self-linking number, that admit only overtwisted contact branched covers. As a direct consequence, we obtain an infinite family of transverse knots in $(\mathbb{S}^3,\xi_{std})$ that are not transverse-universal, although they are universal in the topological sense.

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Sebastian Zapata. 2024-02-19. On transverse-universality of twist knots. https://arxiv.org/abs/2402.12585

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