DGA maps Induced by Decomposable Fillings with Z-coefficients

Abstract

To every Legendrian link in R3, we can assign a differential graded algebra (DGA) called the Chekanov-Eliashberg DGA. An exact Lagrangian cobordism between two Legendrian links induces a DGA map between the corresponding Chekanov-Eliashberg DGAs, and this association is functorial. This DGA map was written down explicity for exact, decomposable Lagrangian fillings as Z_2-count of certain pseudoholomorphic disks by Ekholm, Honda, and K ́alm ́an, and this was combinatorially upgraded to an integral count by Casals and Ng. However, this upgrade only assigned an automorphism class of DGA maps. We approach the same problem of integral lifts by a different strategy, first done for the differential in the Chekanov-Eliashberg DGA by Ekholm, Etnyre, and Sullivan. Here, we find the precise DGA maps for all exact, decomposable Lagrangian cobordisms through this more analytic method.