Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57Q45, 57M25

Retrieve articles in all journals with MSC: 57Q45, 57M25

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society