Coxeter quotients of knot groups through 16 crossings

TL;DR

This paper computes explicit Coxeter quotients for a large class of knot groups up to 16 crossings, verifying a key conjecture and providing a computational tool for future research.

Contribution

It introduces a method to find maximal rank Coxeter quotients for knot groups and verifies the Meridional Rank Conjecture for these knots.

Findings

Verified the Meridional Rank Conjecture for 595,515 knots up to 16 crossings.

Calculated bridge numbers for these knots.

Provided a computational tool for analyzing knots beyond 16 crossings.

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.