Good involutions of conjugation subquandles and core quandles are characterized by central-valued functions, with algorithms, enumeration data, new CNS-quandle families, and a category equivalence between racks and Legendrian racks.
On Core Quandles
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abstract
We characterize several properties of core quandles in terms of the properties of their underlying groups. Specifically, we characterize connected cores providing an answer to an open question in \cite{saito} and present a standard homogeneous representation for them, which allows us to prove that simple core quandles are primitive.
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Good involutions of conjugation subquandles
Good involutions of conjugation subquandles and core quandles are characterized by central-valued functions, with algorithms, enumeration data, new CNS-quandle families, and a category equivalence between racks and Legendrian racks.