An Unknotting Index for Virtual Links

Abstract

Given a virtual link diagram $D$, we define its unknotting index $U(D)$ to be minimum among $(m,n)$ tuples, where $m$ stands for the number of crossings virtualized and $n$ stands for the number of classical crossing changes, to obtain a trivial link diagram. By using span of a diagram and linking number of a diagram we provide a lower bound for unknotting index of a virtual link. Then using warping degree of a diagram, we obtain an upper bound. Both these bounds are applied to find unknotting index for virtual links obtained from pretzel links by virtualizing some crossings

19 pages, 11 figures