Quandle Identities and Homology
Geometric Topology
2016-03-01 v1
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 -cycle, the abelian extension with a -cocycle that vanishes on the -cycle inherits the identity, and a subcomplex is constructed from the identity. Specific identities are examined among small connected quandles.
Cite
@article{arxiv.1602.08535,
title = {Quandle Identities and Homology},
author = {W. Edwin Clark and Masahico Saito},
journal= {arXiv preprint arXiv:1602.08535},
year = {2016}
}