25 citations · 142 across the 59 of their papers we have counts for
76 papers
The groups , braids, and -manifolds
Vassily Olegovich Manturov, Igor Mikhailovich Nikonov
We introduce a family of groups for integer parameters . These groups originate from discussion of braid groups on -surfaces. On the other hand, they turn out to be…
On an invariant of pure braids
V. O. Manturov, I. M. Nikonov
Using the recoupling theory, we define a representation of the pure braid group and show that it is not trivial.
Realisability of , realisability projection, and kernel of the -braid presentation
Vassily Olegovich Manturov
The aim of this article is to prove that the kernel of the map from the pure braid group to the group consists of full twist braids and their exponents.…
Maps from braids to virtual braids and braid representations
V. O. Manturov, I. M. Nikonov
Virtual knot theory has experienced a lot of nice features that did not appear in classical knot theory, e.g., parity and picture-valued invariants. In the present paper we use vir…
A group-valued invariant of knots in the full torus
Vassily Olegovich Manturov, Igor Mikhailovich Nikonov
Knot concordance plays a crucial role in the low dimensional topology. We propose a very elementary techniques which allows one to construct a lot of sliceness obstructions for kno…
Cobordism invariants for knots with two indices
Vassily Olegovich Manturov
We construct an invariant of virtual knots which is a sliceness obstruction and sensitive to the -move. This invariants works if -index of chords is present…