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

DOI:
https://doi.org/10.1090/S0002-9947-1982-0642331-X

MathSciNet review:
642331

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Abstract | References | Similar Articles | Additional Information

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 of two unknotted components in has the *distinct lifting property* for if the lifts of each component to the -fold cover of branched along the other are distinct. The -fold covers of these lifts are homeomorphic, and so gives an example of two distinct knots with the same -fold cover. The above machinery is then used to construct an infinite family of links, each with the distinct lifting property for all .

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DOI:
https://doi.org/10.1090/S0002-9947-1982-0642331-X

Article copyright:
© Copyright 1982
American Mathematical Society