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arXiv · 2507.14551

Multi-virtual braid groups

Valeriy G. Bardakov·Tatyana A. Kozlovskaya·Komal Negi·Madeti Prabhakar
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Abstract

L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and multi-virtual semi-pure braid groups, which are normal subgroups of index $n!$. We give a set of generators and defining relations for these groups, show that multi-virtual (symmetric multi-virtual) braid group is a semi-direct products of multi-virtual pure (symmetric multi-virtual pure) braid group and symmetric group. Also, we introduce multi-welded and multi-unrestricted braid groups and examines structure of three-strand 2-virtual braid group and some its subgroups and quotients. The paper concludes by outlining open problems and suggesting avenues for future research in this area.

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Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi, Madeti Prabhakar. 2025-07-19. Multi-virtual braid groups. https://arxiv.org/abs/2507.14551

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