Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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N-quandles of Spatial Graphs

  • Veronica Backer Peral (Julis-Rabinowitz Center for Public Policy and Finance, Princeton University) ;
  • Blake Mellor (Department of Mathematics, Loyola Marymount University)
  • Received : 2022.08.08
  • Accepted : 2023.03.14
  • Published : 2024.06.30
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Abstract

The fundamental quandle is a powerful invariant of knots, links and spatial graphs, but it is often difficult to determine whether two quandles are isomorphic. One approach is to look at quotients of the quandle, such as the n-quandle defined by Joyce [8]; in particular, Hoste and Shanahan [5] classified the knots and links with finite n-quandles. Mellor and Smith [12] introduced the N-quandle of a link as a generalization of Joyce's n-quandle, and proposed a classification of the links with finite N-quandles. We generalize the N-quandle to spatial graphs, and investigate which spatial graphs have finite N-quandles. We prove basic results about N-quandles for spatial graphs, and conjecture a classification of spatial graphs with finite N-quandles, extending the conjecture for links in [12]. We verify the conjecture in several cases, and also present a possible counterexample.

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References

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