Floer cohomology groups are usually defined over a field of formal functions (a Novikov field). Under certain assumptions, one can equip them with connections, which means operations of differentiation with respect to the Novikov variable. This allows one to write differential equations for Floer cohomology classes. Here, we apply that idea to symplectic cohomology groups associated to Lefschetz fibrations, and establish a relation with enumerative geometry.

中文翻译：

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Fukaya $A_\infty$-与 Lefschetz 纤维化相关的结构。三

Floer 上同调群通常在形式函数域（Novikov 域）上定义。在某些假设下，可以为它们配备连接，这意味着关于诺维科夫变量的微分操作。这允许人们为 Floer 上同调类编写微分方程。在这里，我们将该想法应用于与 Lefschetz 纤维化相关的辛上同调群，并建立与枚举几何的关系。