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articleNo Access
The special rank of virtual knot groups
Journal of Knot Theory and Its Ramifications01 Oct 2020
Preview Abstract
In this paper we introduce the special rank for virtual knots and some properties of this number are studied. Although we do not know if it can be considered as a nontrivial extension of the meridional rank given by [H. U. Boden and A. I. Gaudreau, Bridge number for virtual and welded knots, J. Knot Theory Ramifications24 (2015), Article ID: 1550008] and by [M. Boileau and B. Zimmermann, The $π$ $π$ -orbifold group of a link, Math. Z.200 (1989) 187–208], we prove that classical knots with special rank $2$ $2$ are $2$ $2$ -bridge knots. Therefore, a modified version of the so called Cappell and Shaneson conjecture could be considered.