The average genus of a 2-bridge knot is asymptotically linear

Moshe Cohen; Adam M. Lowrance

The average genus of a 2-bridge knot is asymptotically linear

Geometric Topology 2025-08-19 v1

Authors: Moshe Cohen , Adam M. Lowrance

Abstract

Experimental work suggests that the Seifert genus of a knot grows linearly with respect to the crossing number of the knot. In this article, we use a billiard table model for $2$ -bridge or rational knots to show that the average genus of a $2$ -bridge knot with crossing number $c$ asymptotically approaches $c/4+1/12$ .

Keywords

2-bridge knot rational knot Seifert genus average genus crossing number billiard table model

Cite

@article{arxiv.2205.06122,
  title  = {The average genus of a 2-bridge knot is asymptotically linear},
  author = {Moshe Cohen and Adam M. Lowrance},
  journal= {arXiv preprint arXiv:2205.06122},
  year   = {2025}
}

Comments

17 pages, 2 figures

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