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The Topology of the set of line Transversals

Published 29 May 2022 in math.MG | (2205.14681v2)

Abstract: 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.

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