On detecting the trivial rational 3-tangle.

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 ∞-tangle. The author [4] provided a certain algorithm to detect the ∞-tangle. In this paper, we give a much simpler method to detect the ∞-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. • Bridge arc replacement. • Detecting ∞-tangle. [ABSTRACT FROM AUTHOR]