标题： 谱网络与贝蒂拉格朗日子流形 显示英文标题

标题： Spectral Networks and Betti Lagrangians

摘要： 我们引入并发展了实接触和辛拓扑中谱网络的理论。 首先，我们确立了光滑曲面余切丛中拉格朗日填充的谱网络的存在性及其伪全纯特征描述。这些通过Floer轨迹的绝热退化分析结果以及延续条带的显式计算得以证明。 其次，我们为带有谱网络的拉格朗日填充构造了一个族Floer函子，并证明了它与非交换化函子的等价性。特别是，这意味着用框定的2d-4d BPS态和Gaiotto-Moore-Neitzke非交换化的平行传输都可以实现为相关4d部分缠绕Fukaya范畴的$A_\infty$-操作的一部分。 最后，我们提出了一种新的利用Demazure编织来关联谱网络和拉格朗日填充的构造方法，并展示了谱网络与勒让德接触微分分次代数的增强之间的精确关系。 显示英文摘要

摘要： We introduce and develop the theory of spectral networks in real contact and symplectic topology. First, we establish the existence and pseudoholomorphic characterization of spectral networks for Lagrangian fillings in the cotangent bundle of a smooth surface. These are proven via analytic results on the adiabatic degeneration of Floer trajectories and the explicit computation of continuation strips. Second, we construct a Family Floer functor for Lagrangian fillings endowed with a spectral network and prove its equivalence to the non-abelianization functor. In particular, this implies that both the framed 2d-4d BPS states and the Gaiotto-Moore-Neitzke non-abelianized parallel transport are realized as part of the $A_\infty$-operations of the associated 4d partially wrapped Fukaya categories. To conclude, we present a new construction relating spectral networks and Lagrangian fillings using Demazure weaves, and show the precise relation between spectral networks and augmentations of the Legendrian contact dg-algebra.