6 problems

A 4-move is the local operation on a link diagram that replaces four consecutive half-twists between two strands by the opposite four half-twists. Nakanishi's 4-move conjecture. Ev…

Let two links be 4-equivalent if they are related by a sequence of 4-moves or their inverses, and let the unknot be the trivial knot. 4-move conjecture. Every knot is 4-equivalent…

Let two links be 3-equivalent if they are related by a sequence of 3-moves or their inverses, and call a link trivial if it is a trivial link. 3-move conjecture. Every link is 3-eq…

Przytycki's 4-move conjecture. Any knot is 4-equivalent to the unknot.

A rational $(m,q)$-move is the local move corresponding to the indicated rational tangle, and its inverse and mirror-image moves are also allowed. The Fox $11$-coloring space of a…

A $(2,2)$-move is the local link modification shown in Figure 1.10; two links are $(2,2)$-move equivalent if they are related by such moves, their inverses, and Reidemeister moves.…