51 citations · 254 across the 64 of their papers we have counts for
10 papers · 1 filter
On the lower central series of Baumslag-Solitar groups
V. G. Bardakov, M. V. Neshchadim
We find the lower central series for residually nilpotent Baumslag-Solitar groups, and find the intersection of all terms of the lower central series. Also, we find non-abelian Bau…
On homotopy braids
V. G. Bardakov, V. V. Vershinin, Jie Wu
Homotopy braid group is the subject of the paper. First, linearity of homotopy braid group over the integers is proved. Then we prove that the group homotopy braid group on three s…
Virtually Symmetric representations and marked Gauss diagrams
Valeriy G. Bardakov, Mikhail V. Neshchadim, Manpreet Singh
In this paper, we define the notion of a virtually symmetric representation of representations of virtual braid groups and prove that many known representations are equivalent to v…
Spatial graph as connected sum of a planar graph and a braid
Valeriy G. Bardakov, Akio Kawauchi
In this paper we show that every finite spatial graph is a connected sum of a planar graph, which is a forest, i.e. disjoint union of finite number of trees and a tangle. As a cons…
On 3-strand singular pure braid group
Valeriy G. Bardakov, Tatyana A. Kozlovskaya
In the present paper we study the singular pure braid group for . We find generators, defining relations and the algebraical structure of these groups. In particul…
Quandle cohomology, extensions and automorphisms
Valeriy Bardakov, Mahender Singh
The paper establishes new relationship between cohomology, extensions and automorphisms of quandles. We derive a four term exact sequence relating quandle 1-cocycles, second quandl…