THE ALGEBRA OF RACK AND QUANDLE COHOMOLOGY

DOI10.1142/S0218216511010073zbMath1250.55002arXiv1004.4423OpenAlexW2963564544MaRDI QIDQ3110908

F. J.-B. J. Clauwens

Publication date: 17 January 2012

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

Full work available at URL: https://arxiv.org/abs/1004.4423

zbMATH Keywords

quandletransfer maprackrack homologyquandle homologydelayed Fibonacci conjecturequandle classifying space

Mathematics Subject Classification ID

Related Items (18)

Shifting chain maps in quandle homology and cocycle invariants ⋮ A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation. ⋮ Asymptotic behaviors in the homology of symmetric group and finite general linear group quandles ⋮ On torsion in homology of finite connected quandles ⋮ An explicit description of the second cohomology group of a quandle ⋮ Bialgebraic approach to rack cohomology ⋮ Homology of distributive lattices ⋮ Quandle homotopy invariants of knotted surfaces ⋮ On third homologies of groups and of quandles via the Dijkgraaf-Witten invariant and Inoue-Kabaya map ⋮ Quandle cohomology is a Quillen cohomology ⋮ Homotopical interpretation of link invariants from finite quandles ⋮ Applications of self-distributivity to Yang–Baxter operators and their cohomology ⋮ Unnamed Item ⋮ Cohomology of idempotent braidings with applications to factorizable monoids ⋮ On the rack homology of graphic quandles ⋮ On quandle homology groups of Alexander quandles of prime order ⋮ Distributivity versus associativity in the homology theory of algebraic structures ⋮ The torsion of a finite quasigroup quandle is annihilated by its order

Cites Work

• Homology of dihedral quandles
• A classifying invariant of knots, the knot quandle
• From racks to pointed Hopf algebras
• On rack cohomology.
• The Betti numbers of some finite racks
• Some calculations of cohomology groups of finite Alexander quandles
• An estimate of the triple point numbers of surface-knots by quandle cocycle invariants
• Trunks and classifying spaces
• On the structure of Hopf algebras
• The 3-cocycles of the Alexander quandles \(\mathbb F_q[T/(T-\omega)\)]
• AXIOMS FOR THE GENERALIZED PONTRYAGIN COHOMOLOGY OPERATIONS
• RACKS AND LINKS IN CODIMENSION TWO
• Quandle cohomology and state-sum invariants of knotted curves and surfaces
• Quandles and Monodromy
• James bundles
• Baxter algebras and combinatorial identities. I
• Δ-SETS I: HOMOTOPY THEORY
• Computations of quandle cocycle invariants of knotted curves and surfaces

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