Heptagonal knots and Radon partitions

Details Heptagonal knots and Radon partitions Heptagonal knots and Radon partitions

2010-07-06

arxiv.org/abs/1007.0841v1

Mathematics

Geometric Topology

Scientific paper

We establish a necessary and sufficient condition for a heptagonal knot to be
figure-8 knot. The condition is described by a set of Radon partitions formed
by vertices of the heptagon. In addition we relate this result to the number of
nontrivial heptagonal knots in linear embeddings of the complete graph $K_7$
into $\mathbb{R}^3$.

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