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- Title
Classification of genus 1 virtual knots having at most five classical crossings.
- Authors
Andreevna, Akimova Alena; Matveev, Sergei Vladimirovich
- Abstract
The goal of this paper is to tabulate all genus one prime virtual knots having diagrams with ≤ 5 classical crossings. First, we construct all nonlocal prime knots in the thickened torus T × I which have diagrams with ≤ 5 crossings and admit no destabilizations. Then we use a generalized version of the Kauffman polynomial to prove that all those knots are different. Finally, we convert the knot diagrams in T thus obtained into virtual knot diagrams in the plane.
- Subjects
KNOT theory; TORUS; POLYNOMIALS; GENERALIZATION; PROOF theory
- Publication
Journal of Knot Theory & Its Ramifications, 2014, Vol 23, Issue 6, p-1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S021821651450031X