来自单调拉格朗日转矩的量子同调与 Fukaya 和子

Jack Smith
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引用次数: 0

摘要

让 $L$ 是紧凑交折射流形$X$内的单调拉格朗日环,具有超势 $W_L$。我们证明,几何定义的封闭开图诱导量子同调$operatorname{QH}^*(X)$分解为一个乘积,其中一个因子是雅各布环$\operatorname{Jac} W_L$在$W_L$孤立临界点集合上的局部化。证明包括描述与这个因子相对应的富凯范畴的和--验证镜像对称性的期望--以及建立一个甘纳特拉和桑达风格的自动生成准则,这可能会引起独立的兴趣。我们将我们的结果应用于理解量子同调的结构和约束单调环的可能超势能
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Quantum cohomology and Fukaya summands from monotone Lagrangian tori
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
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