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On the Classification of Knots

1974/08/01 by Kenneth A. Perko · 2 citations
Mathematics · Engineering · #Geometric and Algebraic Topology #Mathematics #Knot (papermaking) #Prime (order theory) #Knot theory #Combinatorics #Table (database) #Crossing number (knot theory) #Pure mathematics #Computer science #Engineering #Data mining

paper · pdf · doi:10.2307/2040074

openalex publication_date 1974/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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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