论文标题
热带福卡亚代数
Tropical Fukaya Algebras
论文作者
论文摘要
我们介绍了Lagrangian Submanifold的Fukaya代数的热带版本。热带图是作为拟切断的伪造磁盘的大规模行为，是在同骨歧管上的多重剪切操作下，该磁层产生了沿着Ionel和Brett Parker的作品的相对正常交叉分隔的切割空间的集合。鉴于在一个切割空间中相对除数的补充中，lagrangian submanifold，伪造的福卡亚代数计数的结构图与刚性热带图有关。我们应用结果来提供各种电势计算，例如在立方体表面和标志品种中的拉格朗日人的计算。进一步的应用程序将出现在续集中。
We introduce a tropical version of the Fukaya algebra of a Lagrangian submanifold. Tropical graphs arise as large-scale behavior of pseudoholomorphic disks under a multiple cut operation on a symplectic manifold that produces a collection of cut spaces each containing relative normal crossing divisors, following works of Ionel and Brett Parker. Given a Lagrangian submanifold in the complement of the relative divisors in one of the cut spaces, the structure maps of the broken Fukaya algebra count broken disks associated to rigid tropical graphs. We apply the results to give various computations of potentials, such as those of Lagrangians in cubic surfaces and flag varieties. Further applications will appear in sequels.
