Abstract:We show that the average or expected absolute value of the signatures of all 2-bridge knots with crossing number $c$ approaches $\sqrt{{2c}/{\pi}}$. Baader, Kjuchukova, Lewark, Misev, and Ray consider a model for 2-bridge knot diagrams indexed by diagrammatic crossing number $n$ and show that the average 4-genus is sublinear in $n$. We build upon this result in two ways to obtain an upper bound for the average 4-genus of a 2-bridge knot: our model is indexed by crossing number $c$ and gives a specific sublinear upper bound of $9.75c/\log c$.
From: Adam Lowrance [view email]
[v1]
Tue, 25 Jun 2024 17:24:24 UTC (36 KB)
[v2]
Thu, 11 Jun 2026 22:58:46 UTC (42 KB)
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