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Coloring Torus Knots by Conjugation Quandles. arXiv:2308.10229

Preprint, arXiv:2308.10229 [math.GR] (2023).
Summary: In the first part of this paper, we present general results concerning the colorability of torus knots using conjugation quandles over any abstract group. Subsequently, we offer a numerical characterization for the colorability of torus knots using conjugation quandles over some particular groups, such as the matrix groups \(GL(2,q)\) and \(SL(2,q)\), the dihedral group, and the symmetric group.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
08A62 Finitary algebras
20N02 Sets with a single binary operation (groupoids)
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