Spherical diagrams and labelled oriented trees

Guenther P Huck, Stephan Rosebrock

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)519-530
Number of pages12
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume137
Issue number3
DOIs
StatePublished - 2007

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Diagram
Asphericity
Oriented Graph
Lemma
Graph in graph theory
Class
Strategy

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 137, No. 3, 2007, p. 519-530.

Research output: Contribution to journalArticle

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