2016/02/27 by Clark, W. Edwin, Saito, Masahico
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1602.08535
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.