3 problems

Let $C_1$, $C_2$, and $C_3$ be any three planar curves. Planar-curve conjecture. They can be used to form the Borromean rings provided that at least one of them is not a circle. Th…

Let three unknotted curves in $\R^3$ be given, and suppose that at least one of them is not a circle. Noncircular obstruction conjecture. It is possible to choose such three curves…

Let $K_1$, $K_2$, and $K_3$ be three unknotted simple closed curves in $\R^3$. Cook's conjecture. They can always be arranged to form the Borromean rings unless they are all circle…