3 citations · 3 across the 5 of their papers we have counts for
5 papers
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…
On universal parity on free two-dimensional knots
Igor Nikonov
We prove that the Gaussian parity on free two-dimensional knots is universal.
Parity functors
Igor Nikonov
A parity is a rule to assign labels to the crossings of knot diagrams in a way compatible with Reidemeister moves. Parity functors can be viewed as parities which provide to each k…
Odd Khovanov homology of principally unimodular bipartite graph-links
Igor Nikonov
We define integral odd Khovanov homology of principally unimodular bipartite graph-links.