51 citations · 254 across the 64 of their papers we have counts for
16 papers · 1 filter
Invariants of Handlebody-Links and Spatial Graphs
V. G. Bardakov, D. A. Fedoseev
A family of quandles is an algebraic construction which was proposed by A. Ishii, M. Iwakiri, Y. Jang, K. Oshiro in 2013. The axioms of these algebraic systems were motivated b…
Extensions of braid group representations to the monoid of singular braids
Valeriy G. Bardakov, Nafaa Chbili, Tatyana A. Kozlovskaya
Given a representation of the braid group , into a group , we are considering the problem of whether it is possible to extend this repres…
Singular braids, singular links and subgroups of camomile type
Valeriy G. Bardakov, Tatyana A. Kozlovskaya
In this paper we find a finite set of generators and defining relations for the singular pure braid group , , that is a subgroup of the singular braid group .…
Multiplication of quandle structures
Valeriy G. Bardakov, Denis A. Fedoseev
We generalise the construction of -family of quandles and -family of quandles which were introduced in the paper of A. Ishii, M. Iwakiri, Y. Jang, K. Oshiro, and find connect…
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…