Two strand twisting

Lambert A'Campo; Sebastian Baader; Livio Ferretti; Levi Ryffel

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arXiv · 2209.06439

Two strand twisting

Lambert A'Campo·Sebastian Baader·Livio Ferretti·Levi Ryffel

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Abstract

We prove that fibred knots cannot be untied with $\bar{t}_{2k}$-moves, for all $k \geq 2$. More generally, we give an upper bound on the number of two strand twist operations that allow to untie a knot with non-trivial HOMFLY polynomial, in terms of the minimal crossing number, and the braid index. As a by-product, we prove that the braid index of a two-bridge knot cannot be lowered by applying $t_{2k}$-moves, for all but finitely many $k \in \mathbb{N}$.

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BibTeX RIS

Lambert A'Campo, Sebastian Baader, Livio Ferretti, Levi Ryffel. 2022-09-14. Two strand twisting. https://arxiv.org/abs/2209.06439

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