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Borromean rays and hyperplanes

Jack S. Calcut

Department of Mathematics, Oberlin College, Oberlin, OH 44074, USA

http://www.oberlin.edu/faculty/jcalcut/.

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Jules R. Metcalf-Burton

Department of Mathematics, Oberlin College, Oberlin, OH 44074, USA

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Taylor J. Richard

Department of Mathematics, Oberlin College, Oberlin, OH 44074, USA

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, and

Liam T. Solus

Department of Mathematics, University of Kentucky, Patterson Office Tower Room 722, Lexington, KY 40504, USA

http://www.ms.uky.edu/~solusl.

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https://doi.org/10.1142/S0218216514500205Cited by:1 (Source: Crossref)

Abstract

Three disjoint rays in ℝ³ 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.

Keywords:

AMSC: 57M30, 57R52, 57M05

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