拉格朗日量的Maurer-Cartan变形
Maurer-Cartan deformation of Lagrangians
摘要：
拉格朗日$L$的Maurer-Cartan代数是将Floer复形$CF(L,L;Λ)$的变形编码为$A_\infty$ -代数的代数。证明了Maurer-Cartan代数与$CF(L,L;Λ)$的Koszul对偶dga的$0$次上同调.利用这一识别，证明了当$G$是\emph{dual}到$L$在定义意义上的时，$L$的Maurer-Cartan代数与另一Lagrangian $G$的包裹Floer上同调的完备化的适当子空间之间存在自然同构.鉴于镜像对称，这可以理解为在镜像刚性解析空间中指定与$L$相关联的局部图表。我们研究的想法明确计算的同构几个有趣的例子。
英文摘要：
The Maurer-Cartan algebra of a Lagrangian $L$ is the algebra that encodes the deformation of the Floer complex $CF(L,L;Λ)$ as an $A_\infty$-algebra. We identify the Maurer-Cartan algebra with the $0$-th cohomology of the Koszul dual dga of $CF(L,L;Λ)$. Making use of the identification, we prove that there exists a natural isomorphism between the Maurer-Cartan algebra of $L$ and a suitable subspace of the completion of the wrapped Floer cohomology of another Lagrangian $G$ when $G$ is \emph{dual} to $L$ in the sense to be defined. In view of mirror symmetry, this can be understood as specifying a local chart associated with $L$ in the mirror rigid analytic space. We examine the idea by explicit calculation of the isomorphism for several interesting examples.
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