Representations of virtual braids by automorphisms and virtual knot groups

被引：13
|
作者：
Bardakov, Valeriy G. [1 ,2 ]
Mikhalchishina, Yuliya A. [2 ,3 ]
Neshchadim, Mikhail V. [1 ,3 ]
机构：
[1] Sobolev Inst Math, 4 Ak Koptyuga Ave, Novosibirsk 630090, Russia
[2] Novosibirsk State Agrarian Univ, 160 Dobrolyubova St, Novosibirsk 630039, Russia
[3] Novosibirsk State Univ, 2 Pirogova St, Novosibirsk 630090, Russia
来源：
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2017年 / 26卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
Braids; virtual braids; representations by automorphisms; ALEXANDER GROUPS; INVARIANTS; LINKS;
D O I：
10.1142/S0218216517500031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the present paper, a new representation of the virtual braid group VBn into the automorphism group of free product of the free group and free abelian group is constructed. This representation generalizes the previously constructed ones. The fact that the previously known representations are not faithful for n >= 4 is verified. Using representations of VBn, a virtual link group is defined. Also representations of the welded braid group WBn are constructed and the welded link group is defined.
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页数：17
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