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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},
pages = {191--240},
publisher = {Springer-Verlag},
volume = {112},
year = {2010},
doi = {10.1007/s10240-010-0028-5},
mrnumber = {2737980},
zbl = {1215.53078},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-010-0028-5/}
}
TY - JOUR AU - Abouzaid, Mohammed TI - A geometric criterion for generating the Fukaya category JO - Publications Mathématiques de l'IHÉS PY - 2010 SP - 191 EP - 240 VL - 112 PB - Springer-Verlag UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-010-0028-5/ DO - 10.1007/s10240-010-0028-5 LA - en ID - PMIHES_2010__112__191_0 ER -
%0 Journal Article %A Abouzaid, Mohammed %T A geometric criterion for generating the Fukaya category %J Publications Mathématiques de l'IHÉS %D 2010 %P 191-240 %V 112 %I Springer-Verlag %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-010-0028-5/ %R 10.1007/s10240-010-0028-5 %G en %F 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
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