Coxeter quotients of knot groups through 16 crossings

Alexandra Kjuchukova; Nathaniel Morrison; Ryan Blair

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Coxeter quotients of knot groups through 16 crossings

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arxiv 2208.09032 v1 pith:EKKMHV4T submitted 2022-08-18 math.GT

Ryan Blair , Alexandra Kjuchukova , Nathaniel Morrison This is my paper · ORCID

classification math.GT

keywords coxetercrossingsknotsquotientsconjecturegroupsknotmeridional

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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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