3 citations · 3 across the 5 of their papers we have counts for
5 papers · 1 filter
The crossing and the arc from the topological viewpoint
Igor Nikonov
The combinatorial approach to knot theory treats knots as diagrams modulo Reidemeister moves. Many constructions of knot invariants (e.g., index polynomials, quandle colorings, etc…
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.
Local transformations and functorial maps
Igor Nikonov
Picture-valued invariants are the main achievement of parity theory by V.O. Manturov. In the paper we give a general description of such invariants which can be assigned to a parit…
Odd Khovanov homology of principally unimodular bipartite graph-links
Igor Nikonov
We define integral odd Khovanov homology of principally unimodular bipartite graph-links.