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

2022/05/12 by Moshe Cohen, Cohen, Moshe, Adam M. Lowrance +1
Mathematics · #57K10 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2205.06122

openalex publication_date 2022/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

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• Genera and crossing numbers of 2-bridge knots
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• Average signature and 4-genus of 2-bridge knots
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