An A∞-Structure for Lines in a Plane
An A∞-Structure for Lines in a Plane
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平面内直线的 A∞ 结构
DOI：
10.1093/imrn/rnp074
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发表时间：
2009
影响因子：
1
通讯作者：
H. Kajiura
中科院分区：
文献类型：
--
作者：
H. Kajiura
作为与几何相关的A ∞ -结构的一个显式例子，我们对中的多条线（拉格朗日量）的福谷范畴显式地构造了一个A ∞ -结构，即我们还定义了非横截A ∞ -积.构造了A ∞范畴，使得它是与DeRham型微分分次范畴A ∞ -同伦等价的.这种构造的动机是（二）环面的同调镜像对称，其中是一个二环面的覆盖空间。该策略是基于通过同调扰动理论的莫尔斯同伦理论的代数重构，如Kontsevich和Soibelman [23]所讨论的。
As an explicit example of an A ∞ -structure associated with geometry, we construct explicitly an A ∞ -structure for a Fukaya category of finitely many lines (Lagrangians) in , i.e. we also define nontransversalA ∞ -products. The A ∞ category is constructed so that it is A ∞ -homotopy equivalent to a differential graded category of DeRham type. This construction is motivated by homological mirror symmetry of (two-)tori, where is the covering space of a two-torus. The strategy is based on an algebraic reformulation of Morse homotopy theory through homological perturbation theory as discussed by Kontsevich and Soibelman [23].