Simply connected latin quandles

Marco Bonatto; Petr Vojtěchovský

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arXiv · 1611.00936

Simply connected latin quandles

Marco Bonatto·Petr Vojtěchovský

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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 Graña for quandles of prime size) and that finite doubly transitive quandles of order different from $4$ are simply connected.

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BibTeX RIS

Marco Bonatto, Petr Vojtěchovský. 2018-08-03. Simply connected latin quandles. https://arxiv.org/abs/1611.00936

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