Studying Links via Plats: The Unlink

Deepisha Solanki

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arXiv · 2308.00732

Studying Links via Plats: The Unlink

Deepisha Solanki

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Abstract

Our main result is a version of Birman's theorem about equivalence of plats, which does not involve stabilization, for the unlink. We introduce the pocket and flip moves, which modify a plat without changing its link type or bridge index. Theorem 1 shows that using the pocket and flip moves, one can simplify any closed $n$-plat presentation of the unknot to the standard 0-crossing diagram of the unknot, through a sequence of plats of non-increasing bridge index. The theorem readily generalises to the case of the unlink.

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Deepisha Solanki. 2023-08-01. Studying Links via Plats: The Unlink. https://arxiv.org/abs/2308.00732

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