51 citations · 254 across the 64 of their papers we have counts for
7 papers · 1 filter
On the lower central series of some virtual knot groups
Valeriy G. Bardakov, Neha Nanda, Mikhail V. Neshchadim
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…
Structural aspects of twin and pure twin groups
Valeriy Bardakov, Mahender Singh, Andrei Vesnin
The twin group is a Coxeter group generated by involutions and the pure twin group is the kernel of the natural surjection of onto the symmetric group on $…
Exterior and symmetric (co)homology of groups
Valeriy G. Bardakov, Mikhail V. Neshchadim, Mahender Singh
The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite g…
On homotopy aspects and cablings of virtual pure braid groups
Valeriy G. Bardakov, Roman Mikhailov, Jie Wu
By exploring simplicial structure of pure virtual braid groups, we give new connections between the homotopy groups of the 3-sphere and the virtual braid groups that are related to…
Free quandles and knot quandles are residually finite
Valeriy G. Bardakov, Mahender Singh, Manpreet Singh
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residu…
Groups of virtual trefoil and Kishino knots
V. G. Bardakov, Yu. A. Mikhalchishina, M. V. Neshchadim
In the paper of Yu. A. Mikhalchishina for an arbitrary virtual link three groups , , and were defined. In the present paper these groups…