Coxeter quotients of knot groups through 16 crossings

2022/08/18 by Ryan Blair, Blair, Ryan, Alexandra Kjuchukova +3 · 2 citations
Mathematics · #57M05 #57M25 #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2208.09032

openalex publication_date 2022/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Whitehead doubling, rank estimate and nonembeddability of contractible open manifolds
• New Upper Bounds for Stick Numbers

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