Groups of the virtual trefoil and Kishino knots

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

Результат исследования: Научные публикации в периодических изданияхстатья

1 Цитирования (Scopus)

Аннотация

In the paper [13], for an arbitrary virtual link L, three groups G1,r(L), r > 0, G2(L) and G3(L) were defined. In the present paper, these groups for the virtual trefoil are investigated. The structure of these groups are found out and the fact that some of them are not isomorphic to each other is proved. Also, we prove that G3 distinguishes the Kishino knot from the trivial knot. The fact that these groups have the lower central series which does not stabilize on the second term is noted. Hence, we have a possibility to study these groups using quotients by terms of the lower central series and to construct representations of these groups in rings of formal power series. It allows to construct an invariants for virtual knots.

Язык оригиналаанглийский
Номер статьи1842009
Число страниц20
ЖурналJournal of Knot Theory and its Ramifications
Том27
Номер выпуска13
DOI
СостояниеОпубликовано - 1 ноя 2018

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