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Quandle coloring quivers of \((p,2)\)-torus links. (English) Zbl 1500.57001

A quandle coloring quiver is a quiver structure on the set of quandle colorings of an oriented link by a finite quandle, and was introduced recently by K. Cho and S. Nelson [J. Knot Theory Ramifications 28, No. 1, Article ID 1950001, 12 p. (2019; Zbl 1420.57032)]. Let \(X\) be a finite quandle and \(K\) an oriented link in 3-space. For any set of quandle homomorphisms \(S \subseteq \operatorname{Hom}(X,X)\), the associated quandle coloring quiver, denoted \(Q_X^S (K)\), is the directed graph with a vertex \(v_f\) for every \(f \in \operatorname{Hom}(Q(K ), X)\) and an edge directed from the vertex \(v_f\) to the vertex \(v_g\), whenever \(g = \phi \circ f\) for some \(\phi \in S\). For \(S = \operatorname{Hom}(X, X)\), the quiver is called the full \(X\)-quandle coloring quiver of \(K\). It has been proved in [loc. cit.] that \(Q_X^S (K)\) is a link invariant.
The paper under review determines the structure of the quandle coloring quiver of a \((p,2)\)-torus link with respect to a dihedral quandle of order \(n\).

MSC:

57K10 Knot theory
57K12 Generalized knots (virtual knots, welded knots, quandles, etc.)

Citations:

Zbl 1420.57032
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References:

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