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.

中文翻译：

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Liouville扇区上的协变函数包装Floer理论

我们引入一类具有边界的Liouville流形，我们称其为Liouville扇形。我们定义了包装的Fukaya类别，辛同调性以及Liouville扇形的开-闭图，并且我们证明了这些不变量对于Liouville扇形的包含是协变的。在此基础设置中，遵循了Abouzaid生成标准的局部到全局原则。