The Topology of the set of line Transversals

Otfried Cheong (1) , Xavier Goaoc (2) , Andreas Holmsen (3)

1 CS - Department of Computer Science [KAIST]
2 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
3 Department of Mathematical Sciences, KAIST

We prove that for any set F of n≥2 pairwise disjoint open convex sets in ℝ³, the connected components of the set of lines intersecting every member of F are contractible. The same result holds for directed lines.

Domaines: Géométrie algorithmique [cs.CG]; Topologie générale [math.GN]

Otfried Cheong, Xavier Goaoc, Andreas Holmsen. The Topology of the set of line Transversals. 2022. ⟨hal-03702551⟩