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


A family of links and the Conway calculus

Author: Cole A. Giller
Journal: Trans. Amer. Math. Soc. 270 (1982), 75-109
MSC: Primary 57M25; Secondary 57M12
MathSciNet review: 642331
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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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PII: S 0002-9947(1982)0642331-X
Article copyright: © Copyright 1982 American Mathematical Society

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