Skip to content
DraconiticResearch
Search Sources API
197,693 studies31 sourcesUpdated 59 min ago
PreprintCC BY 4.0arXiv

On pure braids and bonded braids

  • Sofia Lambropoulou
  • Lucrezia Beatrice Lorenzi
Open at sourcePDFDOICite

Abstract

In this paper we investigate the relation between the bonded braid monoid BBn and the group of pure braids Pn, 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 Pn using cyclic relations and clasp generators, and extend them to presentations of Bn. We construct the monoid epimorphism Φ: BBn → Bn, mapping bonds to pure braid generators, which is the main result of the paper. Using the isomorphism from the singular braid monoid SBn to the tight bonded braid monoid BBn, we extend Φ to a new type of epimorphism s Φ: SBn → Bn. The epimorphisms Φ and $s Φ$ are extended to families of epimorphisms Φp, s Φp, p ∈ ℤ.

Related

  1. The crossing matrix and the Burau matrix of pure braids
    Ayaka Shimizu, Yoshiro Yaguchi
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. Cabled braids and their crossing matrices
    Ayaka Shimizu, Yoshiro Yaguchi
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  3. Quasipositive Braids, Presentations, and Garside Structures
    Jacob Guynee
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  4. Braids on the Stranded Cellular Automata Model
    Alexa Renner
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Determinantal representation of colored HOMFLY for double braids
    Ya. Kononov, A. Morozov
    arXivPreprintarXiv licenceFull textGeometry & topologyMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{lambropoulou2026pure,
  title = {{On pure braids and bonded braids}},
  author = {Sofia Lambropoulou and Lucrezia Beatrice Lorenzi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35340},
  eprint = {2609.35340},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35340},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On pure braids and bonded braids
AU  - Sofia Lambropoulou
AU  - Lucrezia Beatrice Lorenzi
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35340
UR  - https://arxiv.org/abs/2609.35340
AB  - 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 → 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 → B_n. The epimorphisms Φ and $s Φ$ are extended to families of epimorphisms Φ_p, s Φ_p, p ∈ ℤ.
ER  -