5 citations · 9 across the 31 of their papers we have counts for
7 papers · 1 filter
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.
Crossing indices, traits and the principle of indistinguishability
Igor Nikonov
A (weak chord) index is a function on the crossings of knot diagrams such that: 1) the index of a crossing does not change under Reidemeister moves; 2) crossings which can be paire…
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…
Khovanov-Lipshitz-Sarkar homotopy type for links in thickened surfaces
Louis H. Kauffman, Igor Mikhailovich Nikonov, Eiji Ogasa
We define a Khovanov-Lipshitz-Sarkar stable homotopy type for the homotopical Khovanov homology of links in the thickened torus after the authors introduced that in the case of hig…