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Spherical diagrams and labelled oriented trees

Published online by Cambridge University Press:  27 June 2008

Günther Huck  and
Stephan Rosebrock
Günther Huck
Affiliation:
Northern Arizona University, Flagstaff, AZ 86011-5717, USA (guenther.huck@nau.edu)
Stephan Rosebrock
Affiliation:
Pädagogische Hochschule, Postfach 111062, 76060 Karlsruhe, Germany (rosebrock@ph-karlsruhe.de)
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 3 , June 2007 , pp. 519 - 530
Copyright
2007 Royal Society of Edinburgh

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