6 problems

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.

Morton–Mond conjecture. A generic knot with crossing number $n$ has at least

Let an arc in $\mathbb{R}^3$ be an embedding of an interval, and call it wild if it is not ambient isotopic to a tame, piecewise-linear arc. A quadrisecant is a line meeting the ar…

Let $\mathbb{R}P^3$ be real projective 3-space, and let a topological plane be the image of the plane at infinity under a homeomorphism of $\mathbb{R}P^3$. A link is non-trivial if…

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…