On Simply Connected Quandles

2025/04/27 by Bonatto, Marco
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2504.19109

Abstract

In this paper we provide an alternative characterization of finite simply connected quandles involving only cocycles with values in abelian groups of prime size. As a corollary of such a characterization and the classification of connected quandles of size p² and p³ we obtain a classification of simply connected quandles of size p² (already obtained with a different method in \citeVV) and p³ for p>3 using a method that works for quandles of size pⁿ for arbitrary n. We also classify the simply connected quandles within two subclasses of finite involutory quandles: nilpotent latin quandles and core quandles.

Related

• Simply connected latin quandles
• Connected quandles of size pq and 4p
• Principal and Doubly Homogeneous Quandles
• On connected quandles of prime power order
• Classification of simple quandles of small order