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Niebrzydowski, M.; Przytycki, J. H.

Homology operations on homology of quandles. (English) Zbl 1219.55003

J. Algebra 324, No. 7, 1529-1548 (2010).
A notion of partial differential operators on rack homology is introduced and used to construct pre-homological and homological operations on rack and quandle homology. Previous results on dihedral quandles, Alexander quandles and Burnside kei are extended, and results on Fibonacci quandles and quasigroup quandles are obtained. Several interesting new conjectures are introduced, with direct verification in small-cardinality cases.
Reviewer: Sam Nelson (Claremont)

Cited in 1 Review
Cited in 13 Documents

MSC:

55N35 Other homology theories in algebraic topology
18G60 Other (co)homology theories (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

dihedral quandle; Alexander quandle; rack; quandle homology; homological operation; quandle partial differential equation

Software:

GAP
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Full Text: DOI arXiv

References:

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