Simply connected latin quandles
Group Theory
2018-08-06 v5
Abstract
A (left) quandle is connected if its left multiplication group acts transitively. In 2014, Eisermann introduced the concept of quandle coverings, corresponding to so-called constant quandle cocycles that form a subset of quandle cocycles. A connected quandle is said to be \emph{simply connected} if it has no nontrivial coverings, or, equivalently, if its second constant cohomology groups are trivial. In this paper we develop a combinatorial approach to constant cohomology. Upon applying our theory, we prove that connected quandles that are affine over cyclic groups are simply connected (extending a result of Gra\~{n}a for quandles of prime size) and that finite doubly transitive quandles of order different from are simply connected.
Keywords
Cite
@article{arxiv.1611.00936,
title = {Simply connected latin quandles},
author = {Marco Bonatto and Petr Vojtěchovský},
journal= {arXiv preprint arXiv:1611.00936},
year = {2018}
}