The average genus of a 2-bridge knot grows linearly with respect to crossing number

Moshe Cohen (SUNY New Paltz)

Abstract: Dunfield et al provide experimental data to suggest that the Seifert genus of a knot grows linearly with respect to crossing number. We prove this holds among 2-bridge knots using Chebyshev billiard table diagrams developed by Koseleff and Pecker. This work builds on results by the author with Krishnan and Even-Zohar and Krishnan on a random model using these diagrams. This work also uses and improves upon results by the author demonstrating a lower bound for the average genus among a weighted collection of 2-bridge knots. This is joint work with Adam Lowrance.