Region unknotting number of $2$-bridge knots

TL;DR

This paper investigates the region unknotting number for various classes of 2-bridge knots, providing explicit values and bounds for these classes to advance understanding of their topological properties.

Contribution

It introduces explicit region unknotting numbers for specific 2-bridge knot classes and establishes a sharp upper bound for all other classes.

Findings

Region unknotting numbers calculated for classes C(m,n), C(m,2,m), C(m,2,m±1), C(2,m,2,n)

Sharp upper bound provided for remaining 2-bridge knot classes

Enhanced understanding of the topological complexity of 2-bridge knots

Abstract

In this paper, we discuss the region unknotting number of different classes of 2-bridge knots. In particular, we provide region unknotting number for the classes of $2$-bridge knots whose Conway notation is $C(m,\ n), C(m,\ 2,\ m),$ $ C(m,\ 2,\ m\pm1)$ and $C(2,\ m,\ 2,\ n)$. By generalizing, we also provide a sharp upper bound for all the remaining classes of $2$-bridge knots.