### 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) |
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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 - Aug 2 2007 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Spherical diagrams and labelled oriented trees'. Together they form a unique fingerprint.

## Cite this

Huck, G., & Rosebrock, S. (2007). Spherical diagrams and labelled oriented trees.

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*,*137*(3), 519-530. https://doi.org/10.1017/S0308210505000053