论文标题
不保留禁忌关系的扁平虚拟辫子的表示
Representations of flat virtual braids which do not preserve the forbidden relations
论文作者
论文摘要
In the paper, we construct a representation $θ:FVB_n\to{\rm Aut}(F_{2n})$ 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.该表示形式对V. Bardakov在虚拟结理论和R. Fenn，D。Ilyutko，L。Kauffman和V. Manturov的虚拟结论和组合结理论中提出的问题提供了积极的答案。使用此表示形式，我们为平面焊接链接构建了一个新组不变。 另外，我们还发现了$ vb_n $中的组$ vp_n \ cap h_n $的一组普通生成器，$ fvp_n \ cap fh_n $ in $ fvb_n $，$ gvp_n \ gvp_n \ cap gh_n $ in $ gvb_n $，在$ gvb_n $中起重要作用，在代表$θ$的Kernel中起重要作用。
In the paper, we construct a representation $θ:FVB_n\to{\rm Aut}(F_{2n})$ 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 $θ$.
