The contact homology of Legendrian submanifolds in R2n+1

We define the contact homology for Legendrian submanifolds in standard contact (2n + 1)-space using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. This homology provides new invariants of Legendrian isotopy which indicate that the theory of Legendrian isotopy is very rich. Indeed, in [4], the homology is used to detect infinite families of pairwise non-isotopic Legendrian submanifolds which are indistinguishable using previously known invariants.