标题： 面向开放-封闭分类枚举不变量：圆作用形式性同态 显示英文标题

标题： Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism

摘要： 卡拉比-丘范畴的分类枚举不变量，作为相关闭弦场理论（SFT）的划分函数编码，当应用于Fukaya范畴时，其猜想等于Gromov-Witten不变量。 该理论的一部分是一个形式性$L_\infty$同态，它依赖于非交换Hodge滤过结构的分裂。 我们的主要结果是提供一个开-闭形式性同态；所涉及的代数结构猜想为开-闭GW不变量提供了栖息地。 我们解释了开-闭同态是如何成为量化卡拉比-丘范畴中一个对象的大型$N$开SFT的要素。 显示英文摘要

摘要： Categorical enumerative invariants of a Calabi-Yau category, encoded as the partition function of the associated closed string field theory (SFT), conjecturally equal Gromov-Witten invariants when applied to Fukaya categories. Part of this theory is a formality $L_\infty$ morphism which depends on a splitting of the non-commutative Hodge filtration. Our main result is providing an open-closed formality morphism; the algebraic structures involved conjecturallygive a home to open-closed GW invariants. We explain how the open-closed morphism is an ingredient towards quantizing the large $N$ open SFT of an object of a Calabi-Yau category.