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arXiv · 2602.06432

Arc shift move and region arc shift move for twisted knots

Tumpa Mahato·Prabhakar Madeti
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Abstract

In this paper, we study the unknotting operation for twisted knots, called arc shift move. First, we find a family of twisted knots with arc shift number $n$ for any given $n \in \mathbb{N}$. Then we define a new unknotting operation, called the region arc shift move for twisted knots and find family of twisted knots whose region arc shift number is less than or equal to $n$ for any given $n \in \mathbb{N}$. Later, we explore bounds for region arc shift number and forbidden number.

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Tumpa Mahato, Prabhakar Madeti. 2026-02-06. Arc shift move and region arc shift move for twisted knots. https://arxiv.org/abs/2602.06432

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