Classification of genus 1 virtual knots having at most five classical crossings
AA Andreevna, SV Matveev - Journal of Knot Theory and Its …, 2014 - World Scientific
AA Andreevna, SV Matveev
Journal of Knot Theory and Its Ramifications, 2014•World ScientificThe 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.
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.
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.
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