N-quandles of links

The fundamental quandle is a powerful invariant of knots and links, but it is difficult to describe in detail. It is often useful to look at quotients of the quandle, especially finite quotients. One natural quotient introduced by Joyce [1] is the n-quandle. Hoste and Shanahan [2] gave a complete li...

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Bibliographic Details
Published in:Topology and its applications 2021-05, Vol.294, p.107662, Article 107662
Main Authors: Mellor, Blake, Smith, Riley
Format: Article
Language:English
Subjects:
Fundamental quandle
N-quandle
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Summary:The fundamental quandle is a powerful invariant of knots and links, but it is difficult to describe in detail. It is often useful to look at quotients of the quandle, especially finite quotients. One natural quotient introduced by Joyce [1] is the n-quandle. Hoste and Shanahan [2] gave a complete list of the knots and links which have finite n-quandles for some n. We introduce a generalization of n-quandles, denoted N-quandles (for a quandle with k algebraic components, N is a k-tuple of positive integers). We conjecture a classification of the links with finite N-quandles for some N, and we prove one direction of the classification.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2021.107662