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On the asphericity of ribbon disc complements


Author: James Howie
Journal: Trans. Amer. Math. Soc. 289 (1985), 281-302
MSC: Primary 57M20; Secondary 20F05, 57Q45
DOI: https://doi.org/10.1090/S0002-9947-1985-0779064-8
MathSciNet review: 779064
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Abstract: The complement of a ribbon $ n$-disc in the $ (n + 2)$-ball has a $ 2$-dimensional spine which shares some of the combinatorial properties of classical knot complement spines. It is an open question whether such $ 2$-complexes are always aspherical. To any ribbon disc we associate a labelled oriented tree, from which the homotopy type of the complement can be recovered, and we prove asphericity in certain special cases described by conditions on this tree. Our main result is that the complement is aspherical whenever the associated tree has diameter at most $ 3$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0779064-8
Keywords: Ribbon discs, aspherical $ 2$-complexes, locally indicable groups
Article copyright: © Copyright 1985 American Mathematical Society

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