Ribbon 2–knot groups of Coxeter type

Harlander, Jens; Rosebrock, Stephan

doi:10.2140/agt.2023.23.2715

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Ribbon $2$–knot groups of Coxeter type

Jens Harlander and Stephan Rosebrock

Algebraic & Geometric Topology 23 (2023) 2715–2733

DOI: 10.2140/agt.2023.23.2715

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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Volume 23, issue 6 (2023)