Abstract:
We extend the Wada representations of the classical braid group to the virtual and welded braid groups. Using the resulting representations, we construct the groups of virtual links and prove that they are link invariants. We give some examples of calculating the groups of torus (virtual) links.
Keywords:
virtual knot groups, Wada representations, invariants of virtual knots.
Citation:
Yu. A. Mikhalchishina, “Generalizations of the Wada representations and virtual link groups”, Sibirsk. Mat. Zh., 58:3 (2017), 641–659; Siberian Math. J., 58:3 (2017), 500–514
\Bibitem{Mik17}
\by Yu.~A.~Mikhalchishina
\paper Generalizations of the Wada representations and virtual link groups
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 3
\pages 641--659
\mathnet{http://mi.mathnet.ru/smj2886}
\crossref{https://doi.org/10.17377/smzh.2017.58.313}
\elib{https://elibrary.ru/item.asp?id=29160455}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 3
\pages 500--514
\crossref{https://doi.org/10.1134/S0037446617030132}
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Linking options:
https://www.mathnet.ru/eng/smj2886
https://www.mathnet.ru/eng/smj/v58/i3/p641
This publication is cited in the following 4 articles:
Bogdan Chuzhinov, Andrey Vesnin, “Representations of Flat Virtual Braids by Automorphisms of Free Group”, Symmetry, 15:8 (2023), 1538
Valeriy G. Bardakov, Mikhail V. Neshchadim, Manpreet Singh, “Virtually symmetric representations and marked Gauss diagrams”, Topology and its Applications, 306 (2022), 107936
V. G. Bardakov, N. Nanda, M. V. Neshchadim, “On the lower central series of some virtual knot groups”, J. Knot Theory Ramifications, 29:9 (2020)
V. G. Bardakov, Yu. A. Mikhalchishina, M. V. Neshchadim, “Groups of the virtual trefoil and Kishino knots”, J. Knot Theory Ramifications, 27:13, SI (2018), 1842009
Citation in format AMSBIB
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