Ribbon 2–knot groups of Coxeter type

Abstract

Wirtinger presentations of deficiency 1 appear in the context of knots, long virtual knots, and ribbon 2-knots. They are encoded by (word) labeled oriented trees and, for that reason, are also called LOT presentations. These presentations are a well known and important testing ground for the validity (or failure) of Whitehead's asphericity conjecture. In this paper we define LOTs of Coxeter type and show that for every given $n$ there exists a (prime) LOT of Coxeter type with group of rank $n$. We also show that label separated Coxeter LOTs are aspherical.