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Ribbon $2$–knot groups of Coxeter type

Jens Harlander and Stephan Rosebrock

Algebraic & Geometric Topology 23 (2023) 2715–2733
Abstract

Wirtinger presentations of deficiency 1 appear in the context of knots, long virtual knots, and ribbon 2–knots. They are encoded by 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. 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.

Dedicated to the memory of Stephen Pride

Keywords
2–knots, Wirtinger presentations, labeled oriented trees, LOT presentations, knot groups, Coxeter groups, asphericity
Mathematical Subject Classification
Primary: 20F05, 20F06, 20F65
Secondary: 57K20, 57K45
References
Publication
Received: 5 March 2021
Revised: 21 December 2021
Accepted: 3 February 2022
Published: 7 September 2023
Authors
Jens Harlander
Department of Mathematics
Boise State University
Boise, ID
United States
Stephan Rosebrock
Pädagogische Hochschule Karlsruhe
Karlsruhe
Germany

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