{
  "abstract": "In this paper we investigate the relation between the bonded braid monoid BBn and the group of pure braids $P_n$, realised by an algebraic analogue of the topological tangle insertion, namely by replacing a bond by (a power of) a pure braid generator. To do so, we provide appropriate presentations for $P_n$ using cyclic relations and clasp generators, and extend them to presentations of $B_n$. We construct the monoid epimorphism $Φ: BB_n \\to Bn$, mapping bonds to pure braid generators, which is the main result of the paper. Using the isomorphism from the singular braid monoid $SB_n$ to the tight bonded braid monoid $BB_n$, we extend $Φ$ to a new type of epimorphism $s Φ: SB_n \\to B_n$. The epimorphisms $Φ$ and $s Φ$ are extended to families of epimorphisms $Φ_p$, $s Φ_p$, $p \\in \\mathbb{Z}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35340",
  "author_total": 2,
  "authors": [
    {
      "name": "Sofia Lambropoulou"
    },
    {
      "name": "Lucrezia Beatrice Lorenzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ba29ycs03kzx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35340",
  "fulltext_url": null,
  "id": "4ba29ycs03kzx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35340",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214703874",
  "pdf_url": "https://arxiv.org/pdf/2609.35340",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ba29ycs03kzx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35340",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35340"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On pure braids and bonded braids",
  "title_text": "On pure braids and bonded braids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/4ba29ycs03kzx",
  "venue": "arXiv",
  "versions": []
}