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Wirtinger Numbers for Virtual Links by Puttipong Pongtanapaisan is a Mathematics article available to read on EtoBox.
What is Wirtinger Numbers for Virtual Links about?
The Wirtinger number of a virtual link is the minimum number of generators of the link group over all meridional presentations in which every relation is an iterated Wirtinger relation arising in a diagram. We prove that the Wirtinger number of a virtual link equals its virtual bridge number. Since the Wirtinger number is algorithmically computable, it gives a more effective way to calculate an upper bound for the virtual bridge number from a virtual link diagram. As an application, we compute upper bounds for the virtual bridge numbers and the quandle counting invariants of virtual knots with 6 or fewer crossings. In particular, we found new examples of nontrivial virtual bridge number one knots, and by applying Satoh’s Tube map to these knots we can obtain nontrivial weakly superslice links.
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It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Puttipong Pongtanapaisan
- Publisher
- World Scientific Publishing Company; World Scientific ; World Scientific Publishing Co; World Scientific Pub Co Pte Lt (ISSN 0218-2165)
- Published
- 2019
- Language
- EN
- Field
- Mathematics (Physical Sciences)