A relative Calabi-Yau structure for the Chekanov-Eliashberg algebra and applications

For an n-dimensional Legendrian submanifold of a contact manifold whose Rabinowitz Floer complex is acyclic we establish a relative (n+1)-Calabi-Yau structure as defined by Brav-Dyckerhoff.
More precisely, the relative Calabi-Yau structure holds for the canonical inclusion of the chains of the based loop space of the Legendrian into the Chekanov-Eliashberg algebra of the same.
The structure can be explicitly computed by counts of pseudoholomorphic polygons in many cases. Under certain conditions this can be used to show that the augmentation variety of the
Legendrian is a holomorphic Lagrangian. This is joint work in progress with N. Legout.