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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On certain fibred ribbon disc pairs


Authors: Iain R. Aitchison and Daniel S. Silver
Journal: Trans. Amer. Math. Soc. 306 (1988), 529-551
MSC: Primary 57M25; Secondary 57N13, 57Q45, 57R65
MathSciNet review: 933305
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Abstract: We prove that for any free group automorphism $ {\phi ^{\ast}}$ having a specified form there exists an invertible ribbon disc pair $ ({B^4},\,{D^2})$ such that the closure of $ {B_4} - \operatorname{nbd} ({D^2})$ fibres over the circle with fibre a handlebody and monodromy equal to $ {\phi ^{\ast}}$. We apply this to obtain results about ribbon $ 1$- and $ 2$-knots.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0933305-5
PII: S 0002-9947(1988)0933305-5
Article copyright: © Copyright 1988 American Mathematical Society