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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 317 (1990), 813-823
  • MSC: Primary 57Q45; Secondary 57M25
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0987168-1
  • MathSciNet review: 987168