Rectangle conditions and families of 3-bridge prime knots

초록

In 2019, Kwon [10] defined a rectangle condition on the bridge sphere for an n bridge decomposition of a knot and showed that if a 3-bridge decomposition of a knot satisfies the rectangle condition, then the knot is a 3-bridge knot. In 2000, Emert and Ernst [4] defined an interesting family of essential alternating rational 3 tangles. In this paper, we show by using the rectangle condition that knots obtained by taking closures on the tangles in [4] are alternating 3-bridge prime knots. This provides infinite families of 3-bridge prime knots. (c) 2020 Elsevier B.V. All rights reserved.

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