标题： 与拉格朗日子流形相关的开-闭德利涅-芒福德场论 显示英文标题

标题： An open-closed Deligne-Mumford field theory associated to a Lagrangian submanifold

摘要： 设$L \subset X$为紧致对称流形中的紧致嵌入的拉格朗日子流形。我们呈现任意亏格的全纯映射在$L$上的模空间作为全局Kuranishi图，推广了Abouzaid-McLean-Smith和Hirschi-Swaminathan的工作。我们利用此来定义一个开-闭的Deligne-Mumford理论，其开亏格零部分是与$L$相关的Fukaya$A_\infty$代数，其闭部分给出了$X$的Gromov--Witten理论。结合Costello的结果，这在从Fukaya范畴获得Gromov--Witten不变量方面有应用。 显示英文摘要

摘要： Let $L \subset X$ be a compact embedded Lagrangian in a compact symplectic manifold. We present the moduli spaces of holomorphic maps of arbitrary genus with boundary on $L$ as a global Kuranishi chart, generalising the work of Abouzaid-McLean-Smith and Hirschi-Swaminathan. We use this to define an open-closed Deligne-Mumford theory whose open genus zero part is the Fukaya $A_\infty$ algebra associated to $L$, and whose closed part gives the Gromov--Witten theory of $X$. Combined with results of Costello, this has applications in obtaining Gromov--Witten invariants from the Fukaya category.