Linking of three triangles in 3-space

08/11/2019

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by   E. Kogan, et al.

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Two triples of pairwise disjoint triangles in 3-space are combinatorially isotopic if one triple can be obtained from the other by a continuous motion during which the triangles remain pairwise disjoint triangles. We present a short elementary proof that the standard triple of triangles is not combinatorially isotopic to the Borromean triple of triangles (aka Valknut). The earlier proof involved the Massey-Rolfsen invariant. We conjecture that any triple of pairwise disjoint triangles in 3-space is combinatorially isotopic to one of the 5 triples listed in the paper.