Arc shift move and region arc shift move for twisted knots

TL;DR

This paper introduces the arc shift move and region arc shift move as new unknotting operations for twisted knots, establishing their properties and bounds for unknotting numbers.

Contribution

It defines the region arc shift move and identifies families of twisted knots with specific unknotting numbers, expanding understanding of unknotting operations.

Findings

Identified families of twisted knots with arbitrary arc shift numbers

Established bounds for region arc shift number and forbidden number

Introduced the region arc shift move as a new unknotting operation

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.