论文标题
无限的许多拉格朗日馅料
Infinitely many Lagrangian fillings
论文作者
论文摘要
我们证明，除了（2，m），（3,3），（3,4）和（3,5）外，标准触点3-Sphere中的所有最大结-TB Legendrian torus链接（n，m）都承认，在标准符号4球中无限地接受许多拉格朗日填充物。这是通过构建无限顺序的拉格朗日和一致性来证明的，该协调诱导模块化组PSL（2，Z）的忠实行动和映射类M（0,4）在与Legendrian链接相关的代数品种的坐标环中。我们的结果表明，存在Lagrangian的一致性与指数增长的亚组，并产生Stein表面的同型，并具有与无限许多不同的较高genus的无限截然不同的精确拉格朗日表面。我们还表明，存在无限的许多卫星和双曲线结，而莱格德里安代表则承认许多精确的Lagrangian填充物。
We prove that all maximal-tb Legendrian torus links (n,m) in the standard contact 3-sphere, except for (2,m),(3,3),(3,4) and (3,5), admit infinitely many Lagrangian fillings in the standard symplectic 4-ball. This is proven by constructing infinite order Lagrangian concordances which induce faithful actions of the modular group PSL(2,Z) and the mapping class group M(0,4) into the coordinate rings of algebraic varieties associated to Legendrian links. Our results imply that there exist Lagrangian concordance monoids with subgroups of exponential-growth, and yield Stein surfaces homotopic to a 2-sphere with infinitely many distinct exact Lagrangian surfaces of higher-genus. We also show that there exist infinitely many satellite and hyperbolic knots with Legendrian representatives admitting infinitely many exact Lagrangian fillings.
