Ribbon 2-knot groups of Coxeter type

Jens Harlander; Stephan Rosebrock

doi:10.2140/agt.2023.23.2715

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arXiv · 2103.01987

Ribbon 2-knot groups of Coxeter type

Jens Harlander·Stephan Rosebrock

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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.

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Jens Harlander, Stephan Rosebrock. 2021-03-02. Ribbon 2-knot groups of Coxeter type. https://doi.org/10.2140/agt.2023.23.2715

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