作为三维空间中线的镜像的尖点双曲拉格朗日子流形
Cusped hyperbolic Lagrangians as mirrors to lines in three-space
AI总结：
本文构造了三维环面余切丛中带孤立锥形奇点的尖点双曲拉格朗日子流形及对应浸入拉格朗日，证明其经局部系统修饰后可作为射影三维空间中直线的同调镜像，同时构造了适配浸入对象的包裹Fukaya范畴。
摘要：
我们在三维环面的余切丛中构造了一个拉格朗日子流形，其到纤维的投影是一条带有单个4价顶点的热带曲线的邻域。该拉格朗日子流形具有孤立锥形奇点，其光滑轨迹微分同胚于最小扭转五分量链环补空间——一个带尖点的双曲3维流形。我们从这个奇异拉格朗日子流形出发构造了一个浸入拉格朗日子流形，并确定了它在包裹Fukaya范畴中无阻碍的条件。我们证明，对于射影三维空间中的一般直线，该浸入拉格朗日子流形上存在一个局部系统，使得包裹Fukaya范畴中对应的对象与支撑在该直线上的导出范畴对象是同调镜像的。在证明过程中，我们构造了一类以拉格朗日浸入为支撑对象的包裹Fukaya范畴，该范畴本身可能具有独立的研究价值。
英文摘要：
We construct a Lagrangian in the cotangent bundle of a 3-torus whose projection to the fiber is a neighborhood of a tropical curve with a single 4-valent vertex. This Lagrangian has an isolated conical singular point, and its smooth locus is diffeomorphic to the minimally-twisted five component chain link complement, a cusped hyperbolic 3-manifold. From this singular Lagrangian, we construct an immersed Lagrangian, and determine when it is unobstructed in the wrapped Fukaya category. We show that for a generic line in projective 3-space, there is a local system on this immersed Lagrangian such that the resulting object of the wrapped Fukaya category is homologically mirror to an object of the derived category supported on the line. In the course of the proof, we construct a version of the wrapped Fukaya category with objects supported on Lagrangian immersions, which may be of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
