Counting Generic Quadrisecants of Polygonal Knots

Aldo-Hilario Cruz-Cota; Teresita Ramirez-Rosas

Counting Generic Quadrisecants of Polygonal Knots

Geometric Topology 2015-04-17 v2

Authors: Aldo-Hilario Cruz-Cota , Teresita Ramirez-Rosas

Abstract

Let $K$ be a polygonal knot in general position with vertex set $V$ . A \emph{generic quadrisecant} of $K$ is a line that is disjoint from the set $V$ and intersects $K$ in exactly four distinct points. We give an upper bound for the number of generic quadrisecants of a polygonal knot $K$ in general position. This upper bound is in terms of the number of edges of $K$ .

Keywords

knot theory

Cite

@article{arxiv.1502.03029,
  title  = {Counting Generic Quadrisecants of Polygonal Knots},
  author = {Aldo-Hilario Cruz-Cota and Teresita Ramirez-Rosas},
  journal= {arXiv preprint arXiv:1502.03029},
  year   = {2015}
}

Comments

8 pages, 1 figure

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