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.
Fundamental generalized Legendrian rack and classical invariants
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abstract
In this paper, we prove that if two Legendrian knots have isomorphic fundamental GL-racks, then either they have the same Thurston-Bennequin number and the same rotation number, or they have the opposite Thurston-Bennequin numbers and opposite rotation numbers.
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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.