Counting Generic Quadrisecants of Polygonal Knots

Abstract

Let $K$ be a polygonal knot in general position with vertex set $V$. A \emph{generic quadrisecant} of $K$ is a line that is disjoint from the set $V$ and intersects $K$ in exactly four distinct points. We give an upper bound for the number of generic quadrisecants of a polygonal knot $K$ in general position. This upper bound is in terms of the number of edges of $K$.

8 pages, 1 figure

References in corpus (1)

• Alternating Quadrisecants of Knots

Cited by in corpus (1)

• Counterexamples to the quadrisecant approximation conjecture