A geometric criterion for generating the Fukaya category

Details A geometric criterion for generating the Fukaya category A geometric criterion for generating the Fukaya category

2010-01-26

arxiv.org/abs/1001.4593v3

Mathematics

Symplectic Geometry

42 pages, 4 figures. Minor changes. Final version to appear in Publ. IHES

Scientific paper

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.

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