A deformation of the Chekanov-Eliashberg DGA algebra using annuli

We introduce an SFT-type invariant for Legendrian knots in R^3, which is a deformation of the Chekanov-Eliashberg differential graded algebra. The differential includes components that count index zero pseudoholomorphic disks with up to two positive punctures, annuli with one positive puncture, and a string topological component. We also describe a combinatorial way to compute the invariant from the Lagrangian projection