Representations of flat virtual braids which do not preserve the forbidden relations Full article
| Journal |
Journal of Knot Theory and its Ramifications
ISSN: 0218-2165 |
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| Output data | Year: 2023, Volume: 32, Number: 4, Article number : 2350093, Pages count : 27 DOI: 10.1142/S0218216523500931 | ||||||||
| Authors |
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| Affiliations |
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Funding (3)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
| 2 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
| 3 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
In the paper, we construct a representation $\theta:FVB_n→{\rm Aut}(F_{2n})$ of the flat virtual braid group $FVB_n$ on $n$ strands by automorphisms of the free group $F_{2n}$ with $2n$ generators which does not preserve the forbidden relations in the flat virtual braid group. This representation gives a positive answer to the problem formulated by V. Bardakov in the list of unsolved problems in virtual knot theory and combinatorial knot theory by R. Fenn, D. Ilyutko, L. Kauffman and V. Manturov. Using this representation we construct a new group invariant for flat welded links. Also we find the set of normal generators of the groups $VP_n\cap H_n$ in $VB_n$, $FVP_n\cap FH_n$ in $FVB_n$, $GVP_n\cap GH_n$ in $GVB_n$, which play an important role in the study of the kernel of the representation $\theta$.
Cite:
Bardakov V.
, Chuzhinov B.
, Emel'yanenkov I.
, Ivanov M.
, Markhinina E.
, Nasybullov T.
, Panov S.
, Singh N.
, Vasyutkin S.
, Yakhin V.
, Vesnin A.
Representations of flat virtual braids which do not preserve the forbidden relations
Journal of Knot Theory and its Ramifications. 2023. V.32. N4. 2350093 :1-27. DOI: 10.1142/S0218216523500931 WOS Scopus РИНЦ OpenAlex
Representations of flat virtual braids which do not preserve the forbidden relations
Journal of Knot Theory and its Ramifications. 2023. V.32. N4. 2350093 :1-27. DOI: 10.1142/S0218216523500931 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Oct 7, 2020 |
| Accepted: | Sep 20, 2023 |
| Published online: | Feb 27, 2024 |
Identifiers:
| Web of science: | WOS:001183905800005 |
| Scopus: | 2-s2.0-85186938742 |
| Elibrary: | 65181941 |
| OpenAlex: | W3092523305 |