Research ArticleNo Access

The special rank of virtual knot groups

Jhon Jader Mira-Albanés

Escuela de Matemáticas, Universidad Nacional de Colombia, Medellín, Colombia

E-mail Address: jjmira@unal.edu.co

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José Gregorio Rodríguez-Nieto

Escuela de Matemáticas, Universidad Nacional de Colombia, Medellín, Colombia

E-mail Address: jgrodrig@unal.edu.co

Corresponding author.

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, and

Olga Patricia Salazar-Díaz

Escuela de Matemáticas, Universidad Nacional de Colombia, Medellín, Colombia

E-mail Address: opsalazard@unal.edu.co

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https://doi.org/10.1142/S0218216520500881Cited by:1 (Source: Crossref)

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.

Keywords:

AMSC: 20E26, 57M05, 57M27, 57Q45

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