7 papers
Homotopy index polynomials for knotoids
Igor Nikonov
We define homotopy index polynomials and a homotopy type of knotoids in an oriented surface, and consider some basic properties of these polynomials. We show that for planar knotoi…
Exotic 4-manifolds and Khovanov-Lipshitz-Sarkar homotopy type
Louis H. Kauffman, Igor M. Nikonov, Eiji Ogasa
We introduce a new diffeomorphism invariant of smooth compact oriented 4-manifolds with a framed oriented 1-link in the boundary, where may be the empty set, and call i…
A generalisation of the Burau representation and groups for classical braids
Vassily Olegovich Manturov, Igor Mikhailovich Nikonov
We consider a certain modification of the group which describes dynamics of point configurations, in particular braids, and define a representation of the modified .…
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…
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…
On skein invariants
Igor Nikonov
A knot invariant is called skein if it is determined by a finite number of skein relations. In the paper we discuss some basic properties of skein invariants and mention some known…