On the warping sum of knots

Slavik Jablan; Ayaka Shimizu

On the warping sum of knots

Geometric Topology 2017-12-21 v1

Authors: Slavik Jablan , Ayaka Shimizu

Abstract

The warping sum $e(K)$ of a knot $K$ is the minimal value of the sum of the warping degrees of a minimal diagram of $K$ with both orientations. In this paper, knots $K$ with $e(K) \le 3$ are characterized, and some knots $K$ with $e(K)=4$ are given.

Keywords

knot theory

Cite

@article{arxiv.1712.07332,
  title  = {On the warping sum of knots},
  author = {Slavik Jablan and Ayaka Shimizu},
  journal= {arXiv preprint arXiv:1712.07332},
  year   = {2017}
}

Comments

10 pages, 6 figures, to appear in JKTR Special Issue on "Self-distributive system and quandle (co)homology theory in algebra and low-dimensional topology, 2017 KIAS Research Station"

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