On the lower central series of some virtual knot groups

On the lower central series of some virtual knot groups Full article

Journal

Journal of Knot Theory and its Ramifications
ISSN: 0218-2165

Output data

Year: 2020, Volume: 29, Number: 9, Article number : 2050065, Pages count : DOI: 10.1142/S0218216520500650

Tags

Knot group; representation; residually nilpotent group; virtual braid group; virtual knot

Authors

Bardakov V.G. ^1,2,3,4 , Nanda N. ⁵ , Neshchadim M.V. ^1,2,4

Affiliations

1	Sobolev Institute of Mathematics
2	Novosibirsk State University
3	Novosibirsk State Agrarian University, Dobrolyubova street 160, Novosibirsk, 630039, Russian Federation
4	Regional Scientific and Educational Mathematical, Center of Tomsk State University, 36 Lenin Ave, Tomsk, Russian Federation
5	Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S. A. S. Nagar, P. O. Manauli, Punjab, 140306, India

We study groups of some virtual knots with small number of crossings and prove that there is a virtual knot with long lower central series which, in particular, implies that there is a virtual knot with residually nilpotent group. This gives a possibility to construct invariants of virtual knots using quotients by terms of the lower central series of knot groups. Also, we study decomposition of virtual knot groups as semi direct product and free product with amalgamation. In particular, we prove that the groups of some virtual knots are extensions of finitely generated free groups by infinite cyclic groups. © 2020 World Scientific Publishing Company.

Bardakov V.G. , Nanda N. , Neshchadim M.V.
On the lower central series of some virtual knot groups
Journal of Knot Theory and its Ramifications. 2020. V.29. N9. 2050065 . DOI: 10.1142/S0218216520500650 WOS Scopus OpenAlex

Web of science:	WOS:000575412300005
Scopus:	2-s2.0-85091820902
OpenAlex:	W3105194497

DB	Citing
Scopus	1
OpenAlex	2