A classifying invariant of knots, the knot quandle

1982/01/01 by David Joyce · 951 citations
Mathematics · #Combinatorics #Geometric and Algebraic Topology #Invariant (physics) #Knot (papermaking) #Knot invariant #Knot theory #Mathematics #Pure mathematics #Quantum invariant

paper · pdf · doi:10.1016/0022-4049(82)90077-9

published in Journal of Pure and Applied Algebra 23(1), 37-65 (Elsevier BV)

openalex publication_date 1982/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Cited by

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• Quantum invariants of framed links from ternary self-distributive cohomology
• A TABLE OF GENUS TWO HANDLEBODY-KNOTS UP TO SIX CROSSINGS
• Subracks and second homology of the conjugacy classes of finite projective special linear groups of degree two
• Braids and branched coverings of dimension three
• A twisted Hopf algebra of finite topological quandles
• Braided finite automata and representation theory
• More Automorphism Groups of Quandles
• Distinguishing Power of 4-Legendrian Permutation Racks
• Holonomy braidings, biquandles and quantum invariants of links with SL₂(\mathbb C) flat connections
• A G-family of quandles and handlebody-knots
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• Modules over quandle spaces and representations of Lie-Yamaguti algebras
• Kei modules and unoriented link invariants
• Extensions of Quandles and Cocycle Knot Invariants
• Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices
• Computations of Quandle Cocycle Invariants of Knotted Curves and Surfaces
• Quandle Cocycle Quivers
• Quaternion Algebras and Invariants of Virtual Knots and Links I: The Elliptic Case
• A Survey of Quantum Enhancements
• Relationship between quandle shadow cocycle invariants and Vassiliev invariants
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• Cohomology of Categorical Self-Distributivity
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• Affine representations of rational and pretzel knots
• Set-theoretic Yang-Baxter cohomology of cyclic biquandles
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• Homology of Yang-Baxter modules
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• Virtual quandle for links in lens spaces
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