Legendrian Products

Abstract

This paper introduces two constructions of Legendrian submanifolds, called the Legendrian product and spinning, and computes their classical invariants, the Thurston-Bennequin invariant and the Maslov class, in R^{2n+1}. These constructions take two Legendrians K,L and returns a product K x L, they generalize other previous constructions in contact topology, such as frontspinning and hypercube tori, and are equivalent in R^{2n+1}. Interestingly, this construction relies upon the explicit embeddings of K,L and not their Legendrian isotopy classes.