A geometric criterion for generating the Fukaya category

Understand

Given a collection of exact Lagrangians in a Liouville manifold, we construct a map from the Hochschild homology of the Fukaya category that they generate to symplectic cohomology.

• Whenever the identity in symplectic cohomology lies in the image of this map, we conclude that every Lagrangian lies in the idempotent closure of the chosen collection.
• The main new ingredients are (1) the construction of operations controlled by discs with two outputs on the Fukaya category, and (2) the Cardy relation.