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Ribbon $2$–knot groups
of Coxeter type
Jens Harlander and Stephan Rosebrock |
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Algebraic & Geometric Topology 23 (2023) 2715–2733
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Abstract |
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Wirtinger presentations of deficiency 1 appear in the context of knots, long virtual knots, and ribbon –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 there exists a prime LOT of Coxeter type with group of rank . We also show that label separated Coxeter LOTs are aspherical. |
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Dedicated to the memory of Stephen Pride |
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Keywords
2–knots, Wirtinger presentations, labeled oriented trees,
LOT presentations, knot groups, Coxeter groups, asphericity
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Mathematical Subject Classification
Primary: 20F05, 20F06, 20F65
Secondary: 57K20, 57K45
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References |
Publication
Received: 5 March 2021
Revised: 21 December 2021
Accepted: 3 February 2022
Published: 7 September 2023
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Authors |
| Jens Harlander | |
| Department of Mathematics Boise State University Boise, ID United States |
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| Stephan Rosebrock | |
| Pädagogische Hochschule
Karlsruhe Karlsruhe Germany |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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