14 citations · 18 across the 5 of their papers we have counts for
4 papers · 1 filter
Non-Reidemeister Knot Theory and Its Applications in Dynamical Systems, Geometry, and Topology
Vassily Olegovich Manturov
Classical knot theory deals with {\em diagrams} and {\em invariants}. By means of horizontal {\em trisecants}, we construct a new theory of classical braids with invariants valued…
Reidemeister Moves and Groups
Vassily Olegovich Manturov
Recently, the author discovered an interesting class of knot-like objects called free knots. These purely combinatorial objects are equivalence classes of Gauss diagrams modulo Rei…
Graphical Constructions for the sl(3), so(3) and G2 Invariants for Virtual Knots, Virtual Braids and Free Knots
Louis Hirsch Kauffman, Vassily Olegovich Manturov
We construct graph-valued analogues of the Kuperberg sl(3) and G2 invariants for virtual knots. The restriction of the sl(3) or G2 invariants for classical knots coincides with the…
Free Knots, Groups, and Finite-Type Invariants
Vassily Olegovich Manturov
Based on a recently introduced by the author notion of {\em parity}, in the present paper we construct a sequence of invariants (indexed by natural numbers ) of long virtual kno…