Delta-Unknotting Number for Two-Bridge Knots

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. We determine the $\Delta$-unknotting numbers for two-bridge knots of type $C(2{\beta }_1,2{\beta }_2,...,2{\beta }_n)$ and type $C(2{\beta }_1,2{\beta }_2,...,2{\beta }_{n-1},2{\beta }_n-1)$, where ${\beta }_i$ is a positive integer for $1\le i\le n$. We also discuss two-bridge knots whose $\Delta$-unknotting number is equal to one.

15 pages, 7 figures, 2 tables