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Quandle coverings and their Galois correspondence

Michael Eisermann (2014)

Fundamenta Mathematicae

This article establishes the algebraic covering theory of quandles. For every connected quandle Q with base point q ∈ Q, we explicitly construct a universal covering p: (Q̃,q̃̃) → (Q,q). This in turn leads us to define the algebraic fundamental group π ( Q , q ) : = A u t ( p ) = g A d j ( Q ) ' | q g = q , where Adj(Q) is the adjoint group of Q. We then establish the Galois correspondence between connected coverings of (Q,q) and subgroups of π₁(Q,q). Quandle coverings are thus formally analogous to coverings of topological spaces, and resemble Kervaire’s...

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