论文标题
拉格朗日人的毛勒 - 卡丹变形
Maurer-Cartan deformation of Lagrangians
论文作者
论文摘要
Lagrangian $ L $的Maurer-Cartan代数是编码浮动复合物$ cf（l，l;λ）$的变形的代数，为$ a_ \ infty $ algebra。我们以$ CF（L，L;λ）$的Koszul Dual DGA的$ 0 $ TH共同体确定Maurer-Cartan代数。利用标识，我们证明了$ L $的Maurer-Cartan代数与合适的子空间之间存在天然同构，这是一个合适的子空间，即在$ g $中\ emph {dual}到$ l $从$ g $ to ph $ l $ l $从$ g $中定义的另一个Lagrangian $ g $的结束浮动的共同体。鉴于镜像对称性，这可以理解为指定与镜子刚性分析空间中$ l $相关的本地图表。我们通过明确计算同构的几个有趣示例来检查这个想法。
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.
