Classification and structure of generalized Legendrian racks

Luc Ta

doi:10.1007/s13366-026-00864-8

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arXiv · 2504.12671

Classification and structure of generalized Legendrian racks

Luc Ta

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Abstract

This paper develops the structure theory of generalized Legendrian racks, which are algebraic structures used to study Legendrian knots. First, we give a group-theoretic characterization of GL-racks. As applications, we classify GL-racks up to order 8 up to isomorphism via an exhaustive search algorithm, and we classify certain infinite families of GL-racks. Then we compute the center of the category of GL-racks and construct an equivalence of categories between racks and GL-quandles. Finally, we study tensor products of racks and GL-racks coming from universal algebra.

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BibTeX RIS

Luc Ta. 2025-04-17. Classification and structure of generalized Legendrian racks. https://doi.org/10.1007/s13366-026-00864-8

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