Representations of flat virtual braids which do not preserve the forbidden relations

Valeriy Bardakov,Bogdan Chuzhinov, Ivan Emel'yanenkov,Maxim Ivanov, Elizaveta Markhinina,Timur Nasybullov, Sergey Panov,Nina Singh,Sergey Vasyutkin, Valeriy Yakhin,Andrei Vesnin

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS(2023)

Cited 0|Views1
No score
Abstract
In the paper, we construct a representation ??? : FVBn -> Aut(F2n) of the flat virtual braid group FVBn on n strands by automorphisms of the free group F2n 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 Bardakov in the list of unsolved problems in virtual knot theory and combinatorial knot theory by Fenn et al.Also we find the set of normal generators of the groups VPn boolean AND Hn in VBn, FVPn boolean AND FHn in FVBn, GVPn boolean AND GHn in GVBn, which play an important role in the study of the kernel of the representation ???.
More
Translated text
Key words
Flat virtual braids,braid-like groups,representations by automorphisms
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined