On detecting the trivial rational 3-tangle

Abstract

An important issue in classifying rational 3-tangles is how to know whether or not a given tangle is the trivial rational 3-tangle called infinity-tangle. The author [4] provided a certain algorithm to detect the infinity-tangle. In this paper, we give a much simpler method to detect the infinity-tangle by using the bridge arc replacement. We hope that this method can help prove many application problems such as a classification of 3-bridge knots.(c) 2023 Elsevier B.V. All rights reserved.