5 citations · 5 across the 9 of their papers we have counts for
14 papers
Maps from knots in the cylinder to flat-virtual knots
V. O. Manturov, I. M. Nikonov
In the present paper, we address the problem how to get a map from knots in the cylinder and on the thickened torus to some (generalisation of) virtual knots called virtual-flat kn…
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…
Crossing tribes of tangles in a thickened surface
Igor Nikonov
Crossings of knot diagrams can be divided into classes (tribes) compatible with Reidemeister moves. Tribes can be considered as localization of the notion of weak chord index intro…
Intersection formulas for parities on virtual knots
Igor Nikonov
We prove that parities on virtual knots come from invariant 1-cycles on the arcs of knot diagrams. In turn, the invariant cycles are determined by quasi-indices on the crossings of…
Parity on based matrices
Igor Nikonov
A parity is a labeling of the crossings of knot diagrams which is compatible with Reidemeister moves. We define the notion of parity for based matrices -- algebraic objects introdu…
On universal parity on free two-dimensional knots
Igor Nikonov
We prove that the Gaussian parity on free two-dimensional knots is universal.