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

 

Construction by isotopy. II


Author: Daniel S. Silver
Journal: Trans. Amer. Math. Soc. 317 (1990), 813-823
MSC: Primary 57Q45; Secondary 57M25
MathSciNet review: 987168
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Abstract: Construction by isotopy is a technique introduced by Iain R. Aitchison for obtaining doubly slice fibered knots in any dimension. We show that if $ k$ is any doubly slice fibered $ (n - 2)$-knot, $ n \geqslant 5$, such that $ {\pi _1}({S^n} - k) \cong Z$, then $ k$ is constructible by isotopy. We also prove that the $ m$-twist-spin of any doubly slice knot is constructible by isotopy. Consequently, there exists a double slice knot constructible by isotopy that is not the double of any disk knot. We also give an example of a doubly slice fibered $ 6$-knot that is not constructible by isotopy.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0987168-1
PII: S 0002-9947(1990)0987168-1
Article copyright: © Copyright 1990 American Mathematical Society