On the trivializing number of positive knots

TL;DR

This paper investigates the trivializing number of minimal diagrams of positive 2-bridge knots and explores its relationship with the unknotting number for certain cases, providing new insights into knot invariants.

Contribution

It determines the trivializing number for all minimal diagrams of positive 2-bridge knots and examines its connection to the unknotting number, advancing understanding of knot invariants.

Findings

Trivializing number computed for all minimal diagrams of positive 2-bridge knots.

Established a relationship between trivializing number and unknotting number for some positive 2-bridge knots.

Provided new results linking diagrammatic and topological knot invariants.

Abstract

In this paper, we show the trivializing number of all minimal diagrams of positive 2-bridge knots and study the relation between the trivializing number and the unknotting number for a part of these knots.