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On the Classification of Knots

Kenneth A. Perko, Jr.
Proceedings of the American Mathematical Society
Vol. 45, No. 2 (Aug., 1974), pp. 262-266
DOI: 10.2307/2040074
Stable URL: http://www.jstor.org/stable/2040074
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Classification of Knots
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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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