Quandle colorings of knots and applications

DOI10.1142/S0218216514500357zbMath1302.57016arXiv1312.3307OpenAlexW3100774870WikidataQ40404026 ScholiaQ40404026MaRDI QIDQ2922966

Mohamed Elhamdadi, W. Edwin Clark, Timothy Yeatman, Masahico Saito

Publication date: 15 October 2014

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.3307

zbMATH Keywords

knotquandlequandle coloring

Mathematics Subject Classification ID

Related Items (24)

Knotted 4-regular graphs: Polynomial invariants and the Pachner moves ⋮ Classification of flat connected quandles ⋮ Involutory biquandles and singular knots and links ⋮ Unnamed Item ⋮ Asymptotic behaviors in the homology of symmetric group and finite general linear group quandles ⋮ The cocycle structure of the Alexander f-quandles on finite fields ⋮ An explicit description of the second cohomology group of a quandle ⋮ Automorphism groups of quandles arising from groups ⋮ Automorphism groups of quandles and related groups ⋮ Connected quandles and transitive groups ⋮ On rack colorings for surface-knot diagrams without branch points ⋮ Singular knots and involutive quandles ⋮ The Gordian distance of handlebody-knots and Alexander biquandle colorings ⋮ Quandles with orbit series conditions ⋮ Embeddings of quandles into groups ⋮ Computing with knot quandles ⋮ Commutator theory for racks and quandles ⋮ Simply connected latin quandles ⋮ Applications of self-distributivity to Yang–Baxter operators and their cohomology ⋮ Efficient Knot Discrimination via Quandle Coloring with SAT and #-SAT ⋮ General constructions of biquandles and their symmetries ⋮ The Chord Index, its Definitions, Applications, and Generalizations ⋮ Positive quandle homology and its applications in knot theory ⋮ Computations of quandle 2-cocycle knot invariants without explicit 2-cocycles

Uses Software

• GAP
• KnotInfo

Cites Work

• Unnamed Item
• Connected quandles associated with pointed abelian groups
• On homotopy groups of quandle spaces and the quandle homotopy invariant of links
• Moves and invariants for knotted handlebodies
• Knot colouring polynomials
• Homology of dihedral quandles
• Nombre de ponts et générateurs méridiens des entrelacs de Montesinos
• A classifying invariant of knots, the knot quandle
• From racks to pointed Hopf algebras
• The Betti numbers of some finite racks
• Trunks and classifying spaces
• Symbolic computation with finite quandles
• ALEXANDER QUANDLE LOWER BOUNDS FOR LINK GENERA
• FINITE MODULES OVER ℤ[t, t^-1]
• ON THE CLASSIFICATION OF QUANDLES OF LOW ORDER
• THE SECOND QUANDLE HOMOLOGY OF THE TAKASAKI QUANDLE OF AN ODD ABELIAN GROUP IS AN EXTERIOR SQUARE OF THE GROUP
• RACKS AND LINKS IN CODIMENSION TWO
• Quandle cohomology and state-sum invariants of knotted curves and surfaces
• QUANDLES AT FINITE TEMPERATURES II
• Extensions of Quandles and Cocycle Knot Invariants
• THE THIRD COHOMOLOGY GROUPS OF DIHEDRAL QUANDLES
• AUTOMORPHISM GROUPS OF QUANDLES
• Quandle coverings and their Galois correspondence

This page was built for publication: Quandle colorings of knots and applications