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Trivializing ribbon links by Kirby moves

Published online by Cambridge University Press:  17 April 2009

Jonathan A. Hillman
Jonathan A. Hillman
Affiliation:
Department of Pure Mathematics, School of General Studies, Australian National University, Canberra, ACT 2600, Australia.
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Abstract

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In this note it is shown that any ribbon link is a sublink of a ribbon link for which surgery on the longitudes gives a connected sum of copies of S1 x S2. In particular there are many links for which the analogue of the knot theoretic Property R fails, and sublinks of homology boundary links need not be homology boundary links. Higher dimensional analogues of these results are also given and it is shown that if n ≥ 2 the group of a ν-component ribbon n-link has a presentation of deficiency ν. Hence there are high dimensional slice knots which are not ribbon knots.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1980 , pp. 21 - 28
Copyright
Copyright © Australian Mathematical Society 1980

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