Twin groups of virtual 2-bridge knots and almost classical knots
The Wirtinger presentation of a knot group is a combinatorial recipe for computing the fundamental group of the complement of a knot from a knot diagram using a base point above the plane of the knot diagram. For classical knots, the groups obtained using base points above and below the plane of the knot diagram are isomorphic, but for virtual knots these groups can be different. In this paper the authors consider the question of which pairs of groups of a certain form can be realized as the upper and lower knot groups of a virtual knot, obtaining a sufficient condition. A virtual knot is \textit{almost classical} if it has a diagram locally admitting an Alexander numbering; the authors give a necessary condition for a virtual knot to be almost classical in terms of the Jones and Miyazawa polynomials and as an application, determine which of the virtual knots in the virtual knot table on the knot atlas are almost classical.
scientific article; zbMATH DE number 6074275
scientific article