We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly functorial with respect to inclusions of Liouville sectors. From this foundational setup, a local-to-global principle for Abouzaid’s generation criterion follows.
|Original language||English (US)|
|Number of pages||128|
|Journal||Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques|
|State||Published - Jun 1 2020|
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