## 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