### Abstract

To prove that certain standard 2-complexes are aspherical we explore a strategy that combines a well-known method based on a graph theoretic lemma of Stallings with a process of reversing the orientation of edges in spherical diagrams. We apply this strategy to labelled-oriented-tree complexes and, more generally, to labelled-oriented-graph (LOG) complexes and obtain classes of aspherical LOG complexes to which, traditionally (without the reversing of edges), Stallings's lemma could not be applied to prove asphericity. These classes contain examples whose asphericity, as far as we know, could not be established by any previous method.

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

Pages (from-to) | 519-530 |

Number of pages | 12 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 137 |

Issue number | 3 |

DOIs | |

State | Published - 2007 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*,

*137*(3), 519-530. https://doi.org/10.1017/S0308210505000053

**Spherical diagrams and labelled oriented trees.** / Huck, Guenther P; Rosebrock, Stephan.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*, vol. 137, no. 3, pp. 519-530. https://doi.org/10.1017/S0308210505000053

}

TY - JOUR

T1 - Spherical diagrams and labelled oriented trees

AU - Huck, Guenther P

AU - Rosebrock, Stephan

PY - 2007

Y1 - 2007

N2 - To prove that certain standard 2-complexes are aspherical we explore a strategy that combines a well-known method based on a graph theoretic lemma of Stallings with a process of reversing the orientation of edges in spherical diagrams. We apply this strategy to labelled-oriented-tree complexes and, more generally, to labelled-oriented-graph (LOG) complexes and obtain classes of aspherical LOG complexes to which, traditionally (without the reversing of edges), Stallings's lemma could not be applied to prove asphericity. These classes contain examples whose asphericity, as far as we know, could not be established by any previous method.

AB - To prove that certain standard 2-complexes are aspherical we explore a strategy that combines a well-known method based on a graph theoretic lemma of Stallings with a process of reversing the orientation of edges in spherical diagrams. We apply this strategy to labelled-oriented-tree complexes and, more generally, to labelled-oriented-graph (LOG) complexes and obtain classes of aspherical LOG complexes to which, traditionally (without the reversing of edges), Stallings's lemma could not be applied to prove asphericity. These classes contain examples whose asphericity, as far as we know, could not be established by any previous method.

UR - http://www.scopus.com/inward/record.url?scp=34547247070&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547247070&partnerID=8YFLogxK

U2 - 10.1017/S0308210505000053

DO - 10.1017/S0308210505000053

M3 - Article

VL - 137

SP - 519

EP - 530

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 3

ER -