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
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.01798
- arXiv:
- arXiv:1806.01798
- Bibcode:
- 2018arXiv180601798K
- Keywords:
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- Mathematics - Geometric Topology;
- 57M25;
- 57M90
- E-Print:
- 19 pages, 11 figures