Montesinos Knots with Delta-Unknotting Number One

Abstract

The $\Delta$-unknotting number for a knot is defined as the minimum number of $\Delta$-moves needed to deform the knot into the trivial knot. In this paper, we discuss Montesinos knots whose $\Delta$-unknotting number is equal to one. We propose a conjectural characterization of Montesinos knots with $\Delta$-unknotting number one and provide examples admitting distinct $\Delta$-moves, each of which deforms the knot into the trivial knot.

arXiv comment9 pages, 12 figures, 3 tables