An L∞L_∞ structure for Legendrian contact homology

For any Legendrian knot or link in , we construct an algebra that can be viewed as an extension of the Chekanov–Eliashberg differential graded algebra. The structure incorporates information from rational symplectic field theory and can be formulated combinatorially. One consequence is the construction of a Poisson bracket on commutative Legendrian contact homology, and we show that the resulting Poisson algebra is an invariant of Legendrian links under isotopy.