Quandle coloring and cocycle invariants of composite knots and abelian extensions

DOI10.1142/S0218216516500243zbMath1359.57005arXiv1407.5803OpenAlexW1947314366WikidataQ37033045 ScholiaQ37033045MaRDI QIDQ2805389

W. Edwin Clark, Leandro Vendramin, Masahico Saito

Publication date: 11 May 2016

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

Full work available at URL: https://arxiv.org/abs/1407.5803

zbMATH Keywords

quandleabelian extensionscoloringscocycle invariantscomposite knotsend monochromatic

Mathematics Subject Classification ID

Related Items

Multi-switches and virtual knot invariants ⋮ The bridge number of surface links and kei colorings ⋮ Knot quandle decompositions ⋮ Algebraic properties of quandle extensions and values of cocycle knot invariants ⋮ The knot quandle of the twist-spun trefoil is a central extension of a Schläfli quandle ⋮ Quandle identities and homology ⋮ Commutator theory for racks and quandles ⋮ Subquandles of affine quandles ⋮ Quandle cohomology, extensions and automorphisms ⋮ Computations of quandle 2-cocycle knot invariants without explicit 2-cocycles

Uses Software

• RiG
• KnotInfo
• GitHub

Cites Work

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• On homotopy groups of quandle spaces and the quandle homotopy invariant of links
• Surfaces in 4-space
• RACKS AND LINKS IN CODIMENSION TWO
• Quandle cohomology and state-sum invariants of knotted curves and surfaces
• Extensions of Quandles and Cocycle Knot Invariants
• GEOMETRIC INTERPRETATIONS OF QUANDLE HOMOLOGY
• THE THIRD COHOMOLOGY GROUPS OF DIHEDRAL QUANDLES
• AUTOMORPHISM GROUPS OF QUANDLES
• Ribbon concordance of surface-knots via quandle cocycle invariants
• Computations of quandle cocycle invariants of knotted curves and surfaces
• Quandle homology groups, their Betti numbers, and virtual knots

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