On sufficiency of the definition of MCQ Alexander pairs in terms of invariants for handlebody-knots

DOI10.1007/s13366-022-00652-0zbMath1528.57006OpenAlexW4284991924MaRDI QIDQ6174572

Tomo Murao

Publication date: 17 August 2023

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13366-022-00652-0

zbMATH Keywords

handlebody-knotcohomologousmultiple conjugation quandleMCQ Alexander pair\(f\)-twisted Alexander matrix

Mathematics Subject Classification ID

Knot polynomials (57K14) Knot theory (57K10) Invariants of 3-manifolds (including skein modules, character varieties) (57K31) Generalized knots (virtual knots, welded knots, quandles, etc.) (57K12)

Cites Work

• A \(G\)-family of quandles and handlebody-knots
• Homology for quandles with partial group operations
• Affine extensions of multiple conjugation quandles and augmented MCQ Alexander pairs
• A multiple conjugation quandle and handlebody-knots
• Moves and invariants for knotted handlebodies
• A classifying invariant of knots, the knot quandle
• Twisted Alexander polynomial for finitely presentable groups
• From racks to pointed Hopf algebras
• On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links
• The fundamental multiple conjugation quandle of a handlebody-link
• Quandle cohomology and state-sum invariants of knotted curves and surfaces
• Linear extensions of multiple conjugation quandles and MCQ Alexander pairs
• Derivatives with Alexander pairs for quandles
• Representations of knot groups and twisted Alexander polynomials

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