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Tabulating knots in the thickened Klein bottle. (English. Russian original) Zbl 1348.57013

Sib. Math. J. 57, No. 3, 542-548 (2016); translation from Sib. Mat. Zh. 57, No. 3, 688-696 (2016).
Summary: We tabulate all knots in the oriented thickened Klein bottle having diagrams with three crossings and less. For proving that the knots are distinct, we use a generalization of the Kauffman bracket polynomial in four variables.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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References:

[1] Kauffman L. H., “State models and the Jones polynomial,” Topology, 26, No. 3, 395-407 (1987). · Zbl 0622.57004 · doi:10.1016/0040-9383(87)90009-7
[2] Drobotukhina Yu. V., “Classification of links in RP3 with at most 6 crossings,” Zap. Nauchn. Sem. LOMI, 193, 39-63 (1991). · Zbl 0747.57004
[3] Akimova A. A. and Matveev S. V., “Classification of low complexity knots in the thickened torus,” Vestnik NGU Ser. Mat. Mekh. Informat., 12, No. 3, 10-21 (2012). · Zbl 1289.57002
[4] Gabrovsek B. and Mroczkowski M., “Knots in the solid torus up to 6 crossings,” J. Knot Theory Ramifications, 21, No. 11, 43 (2012). · Zbl 1278.57006 · doi:10.1142/S0218216512501064
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