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arXiv · 1909.01003

Untwisting 3-strand torus knots

Sebastian Baader·Ian Banfield·Lukas Lewark
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Abstract

We prove that the signature bound for the topological 4-genus of 3-strand torus knots is sharp, using McCoy's twisting method. We also show that the bound is off by at most 1 for 4-strand and 6-strand torus knots, and improve the upper bound on the asymptotic ratio between the topological 4-genus and the Seifert genus of torus knots from 2/3 to 14/27.

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Sebastian Baader, Ian Banfield, Lukas Lewark. 2021-04-02. Untwisting 3-strand torus knots. https://doi.org/10.1112/blms.12335

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