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ASPHERICAL LABELLED ORIENTED TREES AND KNOTS

Published online by Cambridge University Press:  20 January 2009

Günther Huck  and
Stephan Rosebrock
Günther Huck
Affiliation:
Department of Mathematics, Northern Arizona University, Flagstaff, AZ 86011, USA (gph@math.nau.edu)
Stephan Rosebrock
Affiliation:
Fakultät für Mathematik, University of Education, Bismarckstr. 10, D-76133 Karlsruhe, Germany (rosebrock@PH-karlsruhe.de)
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Abstract

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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

Keywords

2-complexesasphericityknot groupslabelled oriented trees
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 2 , June 2001 , pp. 285 - 294
Copyright
Copyright © Edinburgh Mathematical Society 2001