Classification of Knots of Small Complexity in Thickened Tori

Classification of Knots of Small Complexity in Thickened Tori

We present a table of knots in a thickened torus T × I the diagrams of which have less than five crossing points. The knots are constructed by a three-step process: enumeration of regular graphs of degree 4, enumeration of all corresponding knot projections for each graph, and construction of minima...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2014-10, Vol.202 (1), p.1-12
Hauptverfasser: Akimova, A. A., Matveev, S. V.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:We present a table of knots in a thickened torus T × I the diagrams of which have less than five crossing points. The knots are constructed by a three-step process: enumeration of regular graphs of degree 4, enumeration of all corresponding knot projections for each graph, and construction of minimal diagrams. The completeness of the table is proved.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-014-2029-2