论文标题
增强，填充物和集群
Augmentations, Fillings, and Clusters
论文作者
论文摘要
我们通过浮子理论方法研究了积极的辫子Legendrian链接，并证明它们的增强品种是群集K2（又名A-）品种。使用[EHK16]中的Legendrian链接的确切拉格朗日岩来主义，我们证明了一大批精确的Lagrangian Legendrian Legendrian链接填充物，对应于其增强品种的簇种子。我们解决了无限的填充问题，以解决积极的辫子legendrian链接；也就是说，每当积极的辫子Legendrian链接不是ADE类型时，它就会承认无限的许多精确的Lagrangian填充物，直到哈密顿同位素。
We investigate positive braid Legendrian links via a Floer-theoretic approach and prove that their augmentation varieties are cluster K2 (aka. A-) varieties. Using the exact Lagrangian cobordisms of Legendrian links in [EHK16], we prove that a large family of exact Lagrangian fillings of positive braid Legendrian links correspond to cluster seeds of their augmentation varieties. We solve the infinite-filling problem for positive braid Legendrian links; i.e., whenever a positive braid Legendrian link is not of type ADE, it admits infinitely many exact Lagrangian fillings up to Hamiltonian isotopy.
