Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves

Amrendra Gill, Madeti Prabhakar, Andrei Vesnin

Gordian complex of knots was defined by Hirasawa and Uchida as the simplicial complex whose vertices are knot isotopy classes in ${\mathbb{S}}^3$. Later Horiuchi and Ohyama defined G…