Untangling trigonal diagrams

Erwan Brugallé; Pierre-Vincent Koseleff; Daniel Pecker

Untangling trigonal diagrams

Geometric Topology 2014-11-25 v1

Authors: Erwan Brugallé , Pierre-Vincent Koseleff , Daniel Pecker

Abstract

Let $K$ be a link of Conway's normal form $C(m)$ , $m \geq 0$ , or $C(m,n)$ with $mn\textgreater{}0$ , and let $D$ be a trigonal diagram of $K.$ We show that it is possible to transform $D$ into an alternating trigonal diagram, so that all intermediate diagrams remain trigonal, and the number of crossings never increases.

Keywords

knot theory graph theory

Cite

@article{arxiv.1411.6367,
  title  = {Untangling trigonal diagrams},
  author = {Erwan Brugallé and Pierre-Vincent Koseleff and Daniel Pecker},
  journal= {arXiv preprint arXiv:1411.6367},
  year   = {2014}
}

Comments

10p., 24 figs

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