Quandle Identities and Homology

W. Edwin Clark; Masahico Saito

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arXiv · 1602.08535

Quandle Identities and Homology

W. Edwin Clark·Masahico Saito

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Abstract

Quandle homology was defined from rack homology as the quotient by a subcomplex corresponding to the idempotency, for invariance under the type I Reidemeister move. Similar subcomplexes have been considered for various identities of racks and moves on diagrams. We observe common aspects of these identities and subcomplexes; a quandle identity gives rise to a $2$-cycle, the abelian extension with a $2$-cocycle that vanishes on the $2$-cycle inherits the identity, and a subcomplex is constructed from the identity. Specific identities are examined among small connected quandles.

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BibTeX RIS

W. Edwin Clark, Masahico Saito. 2016-02-27. Quandle Identities and Homology. https://arxiv.org/abs/1602.08535

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