6 problems

Montesinos–Nakanishi 3-move conjecture. Every link can be reduced to a trivial link by 3-moves.

Strong Montesinos–Nakanishi conjecture. Any 2-tangle can be reduced, using 3-moves, to one of the four 2-tangles of Figure 1.10. Additional trivial components in the tangles of Fig…

Let a link be $t_3$, $\bar t_4$ equivalent to another link when it can be obtained from it by $t_3$ and $\bar t_4$ moves and isotopy. The $t_3$–$\bar t_4$ trivial-link conjecture.…

Let $L_1$ and $L_2$ be links. Two links are $t_4$, $\bar t_4$ equivalent if one can be obtained from the other by $t_4$ and $\bar t_4$ moves and isotopy. Kawauchi–Nakanishi conject…

A $(2,2)$-move is the local move shown in the source; a $5$-move is described there as a combination of $(2,2)$-moves and their mirror-image $(-2,-2)$-moves. Universal $(2,2)$-move…

Let two links be link-homotopic if one can be obtained from the other by finitely many self-crossing changes. Two links are 4-equivalent if one can be reached from the other by fin…