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2-complexes

Proceedings of the Edinburgh Mathematical Society (1)

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ASPHERICAL LABELLED ORIENTED TREES AND KNOTS
Günther Huck, Stephan Rosebrock
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 44 / Issue 2 / June 2001

Published online by Cambridge University Press:

20 January 2009, pp. 285-294
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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. We present here two classes of diagrammatically reducible labelled oriented trees.
AMS 2000 Mathematics subject classification: Primary 57M20; 20F06; 20F05; 20F32