Borromean rays and hyperplanes
Jack S. Calcut, Jules R. Metcalf-Burton, Taylor J. Richard, and Liam, T. Solus
TL;DR
This paper introduces Borromean rays and hyperplanes in Euclidean 3-space, demonstrating their existence, constructing infinitely many inequivalent examples, and exploring their knotted properties.
Contribution
It constructs uncountably many Borromean rays and hyperplanes, expanding the understanding of knotted structures in Euclidean space.
Findings
Existence of Borromean rays and hyperplanes.
Uncountably many inequivalent examples.
Properties of their knotted unions.
Abstract
Three disjoint rays in euclidean 3-space form Borromean rays provided their union is knotted, but the union of any two components is unknotted. We construct infinitely many Borromean rays, uncountably many of which are pairwise inequivalent. We obtain uncountably many Borromean hyperplanes.
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