N-quandles of links
| Autor: | Riley Smith, Blake Mellor |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Conjecture 010102 general mathematics Geometric Topology (math.GT) 01 natural sciences Mathematics::Algebraic Topology Mathematics::Geometric Topology 010101 applied mathematics Mathematics - Geometric Topology 57K12 Mathematics::Quantum Algebra FOS: Mathematics Geometry and Topology 0101 mathematics Algebraic number Invariant (mathematics) Quotient Mathematics |
| DOI: | 10.48550/arxiv.2012.15478 |
| Popis: | 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 is the $n$-quandle. Hoste and Shanahan 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. Comment: 31 pages, many figures; v2 reframes the definition of the $N$-quandle in terms of algebraic components of the quandle, so it can be applied to any quandle, not just a link quandle; v3 has minor edits |
| Databáze: | OpenAIRE |
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