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.Comment: 42 pages, 4 figures. Minor changes. Final version to appear in Publ.
IHE
