### Abstract

The question of whether ribbon-disc complements-or, equivalently, standard 2-complexes over labelled oriented trees-are aspherical is of great importance for Whitehead's asphericity conjecture and, if solved affirmatively, would imply a combinatorial proof of the asphericity of knot complements. W e present here two classes of diagrammatically reducible labelled oriented trees.

Original language | English (US) |
---|---|

Pages (from-to) | 285-294 |

Number of pages | 10 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 44 |

Issue number | 2 |

State | Published - 2001 |

### Fingerprint

### Keywords

- 2-complexes
- Asphericity
- Knot groups
- Labelled oriented trees

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*44*(2), 285-294.

**Aspherical labelled oriented trees and knots.** / Huck, Guenther P; Rosebrock, Stephan.

Research output: Contribution to journal › Article

*Proceedings of the Edinburgh Mathematical Society*, vol. 44, no. 2, pp. 285-294.

}

TY - JOUR

T1 - Aspherical labelled oriented trees and knots

AU - Huck, Guenther P

AU - Rosebrock, Stephan

PY - 2001

Y1 - 2001

N2 - The question of whether ribbon-disc complements-or, equivalently, standard 2-complexes over labelled oriented trees-are aspherical is of great importance for Whitehead's asphericity conjecture and, if solved affirmatively, would imply a combinatorial proof of the asphericity of knot complements. W e present here two classes of diagrammatically reducible labelled oriented trees.

AB - The question of whether ribbon-disc complements-or, equivalently, standard 2-complexes over labelled oriented trees-are aspherical is of great importance for Whitehead's asphericity conjecture and, if solved affirmatively, would imply a combinatorial proof of the asphericity of knot complements. W e present here two classes of diagrammatically reducible labelled oriented trees.

KW - 2-complexes

KW - Asphericity

KW - Knot groups

KW - Labelled oriented trees

UR - http://www.scopus.com/inward/record.url?scp=23044534210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044534210&partnerID=8YFLogxK

M3 - Article

VL - 44

SP - 285

EP - 294

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 2

ER -