On knots having zero negative unknotting number

TL;DR

This paper introduces an obstruction criterion for knots to have zero negative unknotting number, aiding in understanding which knots can be unknotted solely through positive crossing changes.

Contribution

It provides a new obstruction method for determining when a knot cannot be unknotted with only positive crossing changes, with applications to specific knot classes.

Findings

Obstruction criterion for zero negative unknotting number

Application to particular classes of knots

Enhanced understanding of crossing change effects

Abstract

A knot in the 3-sphere is said to have zero negative unknotting number if it can be transformed into the unknot by performing only positive crossing changes. In this paper, we provide an obstruction for a knot to having zero negative unknotting number, and discuss its application to two classes of knots.