Derivatives of Jones polynomials detect delta moves in virtual knots.

In this work by Victoria Furlow-Sandy Ganzell-Madison Robinson, the authors consider the Δ-move on virtual knots. The Δ-move is a local move on a (virtual) knot diagram which can be expressed as a composition of two crossing changes and one third Reidemeister move. It is known that the Δ-move is an unknotting move for classical knots (not links, in general) but not for virtual knots. In their paper, they construct techniques to detect whether this move trivialises the virtual knot. 

No prerequisites are required. Interested readers may find the following link useful.https://www.worldscientific.com/doi/10.1142/S0218216522500821