论文标题
Legendrian链接和集群代数的微局部理论
Microlocal Theory of Legendrian Links and Cluster Algebras
论文作者
论文摘要
我们显示了准簇$ \ Mathcal {a} $ - 结构和群集Poisson结构在模束束上，通过研究网格斑点图的交替支撑图中的单数支撑，通过研究微层平行的平行平行运输的Lagrangian填充物的杂物填充链链链链链链球链路的链接。该结构是在接触和互合拓扑的方面，表明存在与规范相对拉格朗日骨骼相关的初始种子。特别是，可变群集$ \ MATHCAL {a} $ - 根据双重$ \ Mathbb {l} $ - 可压缩周期的lagrangian填充物的符号拓扑来代表性地表征。在整个工作中介绍了新成分，包括与网格的图形相关的初始编织，沿着不符号图的非方面的簇突变，无糖船体的概念以及微局部摩擦的概念。最后，为洗牌图构建了DT变换的接触几何实现，证明了集群集合的群集二元性。
We show the existence of quasi-cluster $\mathcal{A}$-structures and cluster Poisson structures on moduli stacks of sheaves with singular support in the alternating strand diagram of grid plabic graphs by studying the microlocal parallel transport of sheaf quantizations of Lagrangian fillings of Legendrian links. The construction is in terms of contact and symplectic topology, showing that there exists an initial seed associated to a canonical relative Lagrangian skeleton. In particular, mutable cluster $\mathcal{A}$-variables are intrinsically characterized via the symplectic topology of Lagrangian fillings in terms of dually $\mathbb{L}$-compressible cycles. New ingredients are introduced throughout this work, including the initial weave associated to a grid plabic graph, cluster mutation along a non-square face of a plabic graph, the concept of the sugar-free hull, and the notion of microlocal merodromy. Finally, a contact geometric realization of the DT-transformation is constructed for shuffle graphs, proving cluster duality for the cluster ensembles.
