标题： 从辛几何场论中得到的精化基本容量 显示英文标题

标题： Refined Elementary Capacities from Symplectic Field Theory

摘要： 我们通过在定义中包含关于曲线出现的正渐近圆柱端数量的约束$\ell$，扩展了 McDuff 和 Siegel 给出的容量族。 我们证明了一个四维凸环面域的广义计算公式，该公式在稳定和非稳定情况下提供了新的、有时是精确的嵌入障碍。 该公式对于$\ell = \infty$限制为 McDuff-Siegel 容量，并对于$\ell = 1$限制为 Gutt-Hutchings 容量。 为了验证该公式，我们必须证明凸环面域$X_\Omega$中存在某些曲线，这与 McDuff-Siegel 的方法相比需要一种新的证明方法。 我们在$\partial X_\Omega$上进行颈部拉伸，并利用已知存在于包含$X_\Omega$的适当选择的椭球中的曲线，从而在所得伪全纯建筑的底层获得所需的曲线。 显示英文摘要

摘要： We extend the family of capacities given by McDuff and Siegel by including a constraint $\ell$ on the number of positive asymptotically cylindrical ends of curves showing up in the definition. We prove a generalized computation formula for four-dimensional convex toric domains that offers new, sometimes sharp, embedding obstructions in stabilized and unstabilized cases. The formula restricts to the McDuff-Siegel capacities for $\ell = \infty$ and to the Gutt-Hutchings capacities for $\ell = 1$. To verify the formula, we must prove the existence of certain curves in the convex toric domain $X_\Omega$, and this requires a new method of proof compared to McDuff-Siegel. We neck-stretch along $\partial X_\Omega$ with curves known to exist in a well-chosen ellipsoid containing $X_\Omega$, and we obtain the desired curves in the bottom level of the resulting psuedoholomorphic building.