Generalized Legendrian racks of Legendrian links

A generalized Legendrian rack is a rack equipped with a Legendrian structure, defined as a pair of maps encoding the information of Legendrian Reidemeister moves together with up and down cusps in the front diagram of an oriented Legendrian link. Employing a purely rack theoretic and universal algebraic approach, we associate a generalized Legendrian rack to an oriented Legendrian link, and prove that it remains invariant under Legendrian isotopy. Our construction seems to be an appropriate generalization of the fundamental quandle of the underlying topological link of an oriented Legendrian link. Moreover, it not only recovers recent rack-theoretic invariants for Legendrian links, but also distinguishes infinitely many oriented Legendrian unknots and trefoils.