Heptagonal knots and Radon partitions

2010/07/06 by Youngsik Huh, Huh, Youngsik
Mathematics · #05C10 #57M15 #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:05C10 #msc:57M15 #msc:57M25

paper · pdf · doi:10.48550/arxiv.1007.0841

arxiv created 2010/07/06 · arxiv updated 2010/07/07

Abstract

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 K₇ into ℝ³.

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