arXiv Analytics

Sign in

arXiv:2208.09032 [math.GT]AbstractReferencesReviewsResources

Coxeter quotients of knot groups through 16 crossings

Ryan Blair, Alexandra Kjuchukova, Nathaniel Morrison

Published 2022-08-18Version 1

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.

Comments: 14 pages, 5 figures, 1 footnote
Categories: math.GT
Subjects: 57M25, 57M27, 57M05
Related articles: Most relevant | Search more
arXiv:math/0409529 [math.GT] (Published 2004-09-27, updated 2009-03-06)
A volume form on the SU(2)-representation space of knot groups
arXiv:1812.09539 [math.GT] (Published 2018-12-22)
Quantized $SL(2)$ representations of knot groups
arXiv:1209.4244 [math.GT] (Published 2012-09-19)
Metabelian SL(n,C) representations of knot groups IV: twisted Alexander polynomials

Links

Toolbox