3 problems

A quadrisecant of a knot is a straight line that intersects the knot four times. It is alternating when the four intersection points alternate between the north and south poles of…

Essential quadrisecants conjecture. The figure-8 knot has at least one essential flipped quadrisecant, and the $5_2$ knot has at least one essential simple quadrisecant.

Jin's conjecture. The quadrisecant approximation $\hat{K}$ has the knot type of $K$, and $K$ and $\hat{K}$ have the same set of quadrisecants.