Classification and structure of generalized Legendrian racks

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.

arXiv commentAccepted manuscript. 23 pages + references