Representations of virtual braids by automorphisms and virtual knot groups

Valeriy G. Bardakov; Yuliya A. Mikhalchishina; Mikhail V. Neshchadim

doi:10.1142/S0218216517500031

Representations of virtual braids by automorphisms and virtual knot groups

Valeriy G. Bardakov, Yuliya A. Mikhalchishina, Mikhail V. Neshchadim

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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.

Original language	English
Article number	1750003
Number of pages	17
Journal	Journal of Knot Theory and its Ramifications
Volume	26
Issue number	1
DOIs	https://doi.org/10.1142/S0218216517500031
Publication status	Published - 1 Jan 2017

Keywords

Braids
representations by automorphisms
virtual braids
INVARIANTS
LINKS
ALEXANDER GROUPS

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10.1142/S0218216517500031

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AU - Neshchadim, Mikhail V.

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KW - INVARIANTS

KW - LINKS

KW - ALEXANDER GROUPS

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