Construction by isotopy. II

Silver, Daniel S.

doi:10.1090/S0002-9947-1990-0987168-1

Construction by isotopy. II
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by Daniel S. Silver PDF

Trans. Amer. Math. Soc. 317 (1990), 813-823 Request permission

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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