Title: Quantum cohomology and Fukaya summands from monotone Lagrangian tori Show Chinese title

Title: 量子上同调与从单色拉格朗日环面得到的Fukaya分量

Abstract: Let $L$ be a monotone Lagrangian torus inside a compact symplectic manifold $X$, with superpotential $W_L$. We show that a geometrically-defined closed-open map induces a decomposition of the quantum cohomology $\operatorname{QH}^*(X)$ into a product, where one factor is the localisation of the Jacobian ring $\operatorname{Jac} W_L$ at the set of isolated critical points of $W_L$. The proof involves describing the summands of the Fukaya category corresponding to this factor -- verifying the expectations of mirror symmetry -- and establishing an automatic generation criterion in the style of Ganatra and Sanda, which may be of independent interest. We apply our results to understanding the structure of quantum cohomology and to constraining the possible superpotentials of monotone tori Show Chinese abstract

Abstract: 设$L$是紧致辛流形$X$中的一个单调拉格朗日环面，其超势能为$W_L$。我们证明了一个几何定义的闭开映射将量子上同调$\operatorname{QH}^*(X)$分解为一个乘积，其中一部分是雅可比环$\operatorname{Jac} W_L$在$W_L$的孤立临界点集上的局部化。证明涉及描述与该部分对应的 Fukaya 范畴的和项——验证镜像对称的预期——并建立一种类似于 Ganatra 和 Sanda 的自动生成准则，这可能具有独立的兴趣。我们将这些结果应用于理解量子上同调的结构以及约束单调环面的可能超势能。