A classifying invariant of knots, the knot quandle

1982/01/01 by David Joyce · 84 citations
Mathematics · #Geometric and Algebraic Topology

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

Cited by

• Colouring bijections of finite 3-groups
• Distributivity relations on the binary operations over a fixed set
• Classification of Finite Subquandles in Spherical Quandles
• From affine algebraic racks to Leibniz algebras and Yang–Baxter operators
• Quandle-like Structures From Groups
• Quandle colorings vs. biquandle colorings
• A multiple conjugation biquandle and handlebody-links
• Idempotents and Powers of Ideals in Quandle Rings
• Quandle Coloring Quivers
• Parallelization of Welded Links
• Lifting in a non semisimple world
• Infinitely many pairs of spatial surfaces
• A note on conjugacy search and racks
• 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
• Knot quandle decomposition along a torus
• Rack shadows and their invariants
• 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\n Elliptic Case
• A Survey of Quantum Enhancements
• Relationship between quandle shadow cocycle invariants and Vassiliev invariants
• The shadow nature of positive and twisted quandle cocycle invariants of knots
• Cohomology of Categorical Self-Distributivity
• The column group and its link invariants
• Affine representations of rational and pretzel knots
• Set-theoretic Yang-Baxter cohomology of cyclic biquandles
• Ribbon concordance of surface-knots via quandle cocycle invariants
• Quandles and Lefschetz Fibrations
• Geometric Interpretations of Quandle Homology
• Structure groups and second homology groups of linear Alexander quandles
• Groups versus quandle-like invariants of 3-manifolds
• Latin quandles of size 16p
• Generalizations of Quandle Cocycle Invariants and Alexander Modules from Quandle Modules
• Virtual Links with Finite Medial Bikei
• Generalized virtualization on welded links
• Homogeneous quandles arising from automorphisms of symmetric groups
• Derivations of quandles
• Two- and three-cocycles for Laver tables
• Algebraic Properties of Quandle Extensions and Values of Cocycle Knot Invariants
• Causality Detection via Symplectic Quandles
• Twisted cohomology pairings of knots I; diagrammatic computation
• The knot quandles of Suciu's ribbon n-knots and automorphisms on the free group of rank two
• Good involutions of twisted conjugation subquandles and Alexander quandles
• On Rack Invariants Of Legendrian Knots
• Quantum Cocycle Invariants of Knots from Yang-Baxter Cohomology
• Shifting Homomorphisms in Quandle Cohomology and Skeins of Cocycle Knot Invariants
• Involutory quandles of (2,2,r)-Montesinos links
• Update of "Biquandles of Small Size and some Invariants of Virtual and Welded Knots"
• Detecting Causality with Conjugation Quandles over Dihedral Groups
• Quandle Cohomology and State-sum Invariants of Knotted Curves and Surfaces
• Fundamental Heaps for Surface Ribbons and Cocycle Invariants
• Topological Quandles and Invariants of Links
• Polars and antipodal sets of generalized s-manifolds
• Quantum Enhancements of Involutory Birack Counting Invariants
• Polynomial cocycles of Alexander quandles and applications
• Biquandle cohomology and state-sum invariants of links and surface-links
• Quotient Quandles and the Fundamental Latin Alexander Quandle
• Pointed Racks and Their Applications to Braid Theory
• A free two-generated left distributive algebra of elementary embeddings
• Racks and blocked braids
• Quandle and hyperbolic volume
• Compactness of the space of left orders
• The Classification of Spun Torus Knots
• Fundamental generalized Legendrian rack and classical invariants
• de Rham theory and cocycles of cubical sets from smooth quandles
• Cohomology of Frobenius Algebras and the Yang-Baxter Equation
• Some comparisons of Blanchfield pairings and cohomology pairings of knots
• Computations of quandle cocyle invariants of surface-links using marked graph diagrams
• Toward a classification of finite quandles
• Surfaces, braids, Stokes matrices, and points on spheres
• Link invariants from finite Coxeter racks