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FORMING THE BORROMEAN RINGS OUT OF ARBITRARY POLYGONAL UNKNOTS

HUGH NELSON HOWARDS

Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, USA

https://doi.org/10.1142/S0218216513500831Cited by:0 (Source: Crossref)

Abstract

We prove that given any three polygonal unknots in ℝ³, then we may form the Borromean rings out of them through rigid motions of ℝ³ applied to the individual components together with possible scaling of the components. We also prove that if at least two of the unknots are planar, then we do not need scaling. This is true even for a set of three polygonal unknots that are arbitrarily close to three circles, which themselves cannot be used to form the Borromean rings.

Keywords:

AMSC: 57M25

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