Geodesic
Ribbon 2–knot groups of Coxeter type
Harlander, Jens1 ; Rosebrock, Stephan2
1 Department of Mathematics, Boise State University, Boise, ID, United States
2 Pädagogische Hochschule Karlsruhe, Karlsruhe, Germany
Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2715-2733

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2023.23.2715
Keywords: 2–knots, Wirtinger presentations, labeled oriented trees, LOT presentations, knot groups, Coxeter groups, asphericity

Harlander, Jens 1 ; Rosebrock, Stephan 2

1 Department of Mathematics, Boise State University, Boise, ID, United States
2 Pädagogische Hochschule Karlsruhe, Karlsruhe, Germany 
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Harlander, Jens; Rosebrock, Stephan. Ribbon 2–knot groups of Coxeter type. Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2715-2733. doi: 10.2140/agt.2023.23.2715

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