On Lagrangian cobordisms and the Chekanov-Eliashberg DGA

In this paper, we consider exact Lagrangian cobordisms and the map they induce on the Chekanov-Eliashberg DGAs of their Legendrian ends as defined by Ekholm, Honda, and Kalman. Specifically, we show how to adapt this map to linearizations of the DGA using augmentations. We then show its induced map on linearized Legendrian contact homology is invariant under Lagrangian isotopy under mild hypotheses, as well as its induced map on higher order product structures.