On the Classification of Knots
- 1 August 1974
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 45 (2) , 262-266
- https://doi.org/10.2307/2040074
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 -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.Keywords
This publication has 4 references indexed in Scilit:
- Darstellungen von Knotengruppen und eine KnoteninvarianteAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1970
- Metacyclic Invariants of Knots and LinksCanadian Journal of Mathematics, 1970
- An enumeration of knots and links, and some of their algebraic propertiesPublished by Elsevier ,1970
- On a Certain Numerical Invariant of Link TypesTransactions of the American Mathematical Society, 1965