Highly twisted plat diagrams

Nir Lazarovich; Yoav Moriah; Tali Pinsky

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arXiv · 2111.14231

Highly twisted plat diagrams

Nir Lazarovich·Yoav Moriah·Tali Pinsky

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Abstract

We prove that the knots and links in the infinite set of $3$-highly twisted $2m$-plats, with $m \geq 2$, are all hyperbolic. This should be compared with a result of Futer-Purcell for $6$-highly twisted diagrams. While their proof uses geometric methods our proof is achieved by showing that the complements of such knots or links are unannular and atoroidal. This is done by using a new approach involving an Euler characteristic argument.

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Nir Lazarovich, Yoav Moriah, Tali Pinsky. 2021-11-28. Highly twisted plat diagrams. https://arxiv.org/abs/2111.14231

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