A family of links and the Conway calculus
Author:
Cole A. Giller
Journal:
Trans. Amer. Math. Soc. 270 (1982), 75109
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 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719820642331X
PII:
S 00029947(1982)0642331X
Article copyright:
© Copyright 1982
American Mathematical Society
