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On 3-strand singular pure braid group

Valeriy G. Bardakov

Tomsk State University, pr. Lenina, 36, Tomsk 634050, Russia

Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090, Novosibirsk, Russia

Novosibirsk State University, 2 Pirogova Street, 630090, Novosibirsk, Russia

Novosibirsk State Agrarian University, Dobrolyubova Street, 160, Novosibirsk 630039, Russia

E-mail Address: bardakov@math.nsc.ru

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and

Tatyana A. Kozlovskaya

Regional Scientific and Educational Mathematical, Center of Tomsk State University, pr. Lenina, 36, Tomsk 634050, Russia

E-mail Address: t.kozlovskaya@math.tsu.ru

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https://doi.org/10.1142/S0218216520420018Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue: Proceedings of 6th Russian — Chinese Conference on Knot Theory and Related Topics (Part 1)
Guest Editors: N. Abrosimov, Z. Cheng, L. H. Kauffman, A. Vesnin and Z. Yang

Abstract

In this paper, we study the singular pure braid group ${SP}_{n}$ ${SP}_{n}$ for $n = 2, 3$ $n = 2, 3$ . We find generators, defining relations and the algebraical structure of these groups. In particular, we prove that ${SP}_{3}$ ${SP}_{3}$ is a semi-direct product ${SP}_{3} = {\tilde{V}}_{3} ⋋ ℤ$ ${SP}_{3} = {\tilde{V}}_{3} ⋋ ℤ$ , where ${\tilde{V}}_{3}$ ${\tilde{V}}_{3}$ is an HNN-extension with base group $ℤ^{2} * ℤ^{2}$ $ℤ^{2} * ℤ^{2}$ and cyclic associated subgroups. We prove that the center $Z ({SP}_{3})$ $Z ({SP}_{3})$ of ${SP}_{3}$ ${SP}_{3}$ is a direct factor in ${SP}_{3}$ ${SP}_{3}$ .

Keywords:

AMSC: 20F36, 20E07, 57K12

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