Singular braids, singular links and subgroups of camomile type

2022/12/16 by Valeriy G. Bardakov, Bardakov, Valeriy G., Tatyana A. Kozlovskaya +1 · 2 citations
Mathematics · #20F36 #57M25 #57M27 #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2212.08267

openalex publication_date 2022/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we find a finite set of generators and defining relations for the singular pure braid group SP_n, n ≥ 3, that is a subgroup of the singular braid group SG_n. Using this presentation, we prove that the center of SG_n (which is equal to the center of SP_n for n ≥ 3) is a direct factor in SP_n but it is not a direct factor in SP_n. We introduce subgroups of camomile type and prove that the singular pure braid group SP_n, n ≥ 5, is a subgroup of camomile type in SG_n. Also we construct the fundamental singquandle using a representation of the singular braid monoid by endomorphisms of free guandle. For any singular link we define some family of groups which are invariants of this link.

Cited by

• Algebraic and topological aspects of the singular twin group and its representations
• Multi-virtual braid groups

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