The Topology of the set of line Transversals
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen · arXiv (Cornell University) · 2022
We prove that for any set $F$ of $n\ge 2$ pairwise disjoint open convex sets in $\mathbb{R}^3$, the connected components of the set of lines intersecting every member of $F$ are contractible. The same result holds for directed lines.