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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the classification of knots


Author: Kenneth A. Perko
Journal: Proc. Amer. Math. Soc. 45 (1974), 262-266
MSC: Primary 55A25
MathSciNet review: 0353294
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Abstract: Linking numbers between branch curves of irregular covering spaces of knots are used to extend the classification of knots through ten crossings and to show that the only amphicheirals in Reidemeister's table are the seven identified by Tait in 1884. Diagrams of the 165 prime $ 10$-crossing knot types are appended. (Murasugi and the author have proven them prime; Conway claims proof that the tables are complete.) Including the trivial type, there are precisely 250 prime knots with ten or fewer crossings.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0353294-X
Keywords: Knots with ten crossings, amphicheirality, linking numbers between branch curves of irregular covering spaces of knots
Article copyright: © Copyright 1974 American Mathematical Society