On detecting the trivial rational $3$-tangle

Bo-hyun Kwon

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arXiv · 2303.06998

On detecting the trivial rational $3$-tangle

Bo-hyun Kwon

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Abstract

An important issue in classifying the rational $3$-tangle is how to know whether or not the given tangle is the trivial rational 3-tangle called $\infty$-tangle. The author\cite{1} provided a certain algorithm to detect the $\infty$-tangle. In this paper, we give a much simpler method to detect the $\infty$-tangle by using the $\textit{bridge arc replacement}$. We hope that this method can help prove many application problems such as the classification of $3$-bridge knots.

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Bo-hyun Kwon. 2023-03-13. On detecting the trivial rational $3$-tangle. https://arxiv.org/abs/2303.06998

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