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 on the Fukaya category controlled by discs with two outputs, and (2) the Cardy relation.
@article{PMIHES_2010__112__191_0,
author = {Abouzaid, Mohammed},
title = {A geometric criterion for generating the Fukaya category},
journal = {Publications Math\'ematiques de l'IH\'ES},
volume = {112},
year = {2010},
pages = {191-240},
doi = {10.1007/s10240-010-0028-5},
mrnumber = {2737980},
zbl = {1215.53078},
language = {en},
url = {http://dml.mathdoc.fr/item/PMIHES_2010__112__191_0}
}
Abouzaid, Mohammed. A geometric criterion for generating the Fukaya category. Publications Mathématiques de l'IHÉS, Tome 112 (2010) pp. 191-240. doi : 10.1007/s10240-010-0028-5. http://gdmltest.u-ga.fr/item/PMIHES_2010__112__191_0/
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