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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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A family of links and the Conway calculus
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by Cole A. Giller PDF
Trans. Amer. Math. Soc. 270 (1982), 75-109 Request permission

Abstract:

In 1969, J. H. Conway gave efficient methods of calculating abelian invariants of classical knots and links. The present paper includes a detailed exposition (with new proofs) of these methods and extensions in several directions. The main application given here is as follows. A link $L$ of two unknotted components in ${S^3}$ has the distinct lifting property for $p$ if the lifts of each component to the $p$-fold cover of ${S^3}$ branched along the other are distinct. The $p$-fold covers of these lifts are homeomorphic, and so $L$ gives an example of two distinct knots with the same $p$-fold cover. The above machinery is then used to construct an infinite family of links, each with the distinct lifting property for all $p \geqslant 2$.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 270 (1982), 75-109
  • MSC: Primary 57M25; Secondary 57M12
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0642331-X
  • MathSciNet review: 642331