# Coxeter groups and meridional rank of links

## TL;DR

This paper proves the meridional rank conjecture for certain classes of links, using Coxeter group quotients and combinatorial tools to establish bounds on link invariants.

## Contribution

It introduces new methods combining Coxeter quotients and Wirtinger numbers to verify the meridional rank conjecture for twisted and arborescent links.

## Key findings

- Meridional rank conjecture verified for twisted links
- Lower bounds derived from Coxeter quotients
- Upper bounds obtained via Wirtinger numbers

## Abstract

We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These links are substantial generalizations of pretzels and two-bridge links, respectively. Lower bounds on meridional rank are obtained via Coxeter quotients of the groups of link complements. Matching upper bounds on bridge number are found using the Wirtinger numbers of link diagrams, a combinatorial tool developed by the authors.