Some Baumslag-Solitar groups are two bridges virtual knots

J. G. Rodríguez; O. P. Salazar-Díaz; J. J. Mira

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arXiv · 1511.03389

Some Baumslag-Solitar groups are two bridges virtual knots

J. G. Rodríguez·O. P. Salazar-Díaz·J. J. Mira

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Abstract

In this paper we give necessary conditions on group presentations, with two generators and one relator, in order to be the group of a virtual knot diagram. Although those conditions are not enough, we use them to determine, completely, whether or not a Baumslag-Solitar group is the group of a $2$-bridge virtual knot. Moreover, we present a combinatorial proof of the fact that these groups are not $2$-bridge classical knot groups.

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J. G. Rodríguez, O. P. Salazar-Díaz, J. J. Mira. 2015-11-11. Some Baumslag-Solitar groups are two bridges virtual knots. https://arxiv.org/abs/1511.03389

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