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math.GT2022
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…
math.GT2022
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…
math.GT2022
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…