Coxeter quotients of knot groups through 16 crossings

Ryan Blair; Alexandra Kjuchukova; Nathaniel Morrison

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arXiv · 2208.09032

Coxeter quotients of knot groups through 16 crossings

Ryan Blair·Alexandra Kjuchukova·Nathaniel Morrison

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Abstract

We find explicit maximal rank Coxeter quotients for the knot groups of 595,515 out of the 1,701,936 knots through 16 crossings. We thus calculate the bridge numbers and verify Cappell and Shaneson's Meridional Rank Conjecture for these knots. In addition, we provide a computational tool for establishing the conjecture for knots beyond 16 crossings whose meridional ranks can be detected via finite Coxeter quotients.

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Ryan Blair, Alexandra Kjuchukova, Nathaniel Morrison. 2022-08-18. Coxeter quotients of knot groups through 16 crossings. https://arxiv.org/abs/2208.09032

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