论文标题
ECH能力的基本替代方案
An elementary alternative to ECH capacities
论文作者
论文摘要
ECH能力是一系列符号四序数的数值不变性，这些序列具有（有时）对符号嵌入的障碍物。这些能力是使用嵌入式接触同源性定义的，并确定其基本属性当前需要Seiberg-witten理论。在本说明中，我们仅使用全态曲线的基本概念在四个维度中定义了一个新的符号能力序列。新容量满足与ECH能力相同的基本属性，并同意已计算后者的主要示例的ECH能力，即凸出和凹形旋转圆环域。新的容量也可用于将符号嵌入到封闭的互合式四元中。这项工作的灵感来自最近的McDuff-Siegel的预印本，从而提供了与Rational SFT的类似基本替代方案。
The ECH capacities are a sequence of numerical invariants of symplectic four-manifolds which give (sometimes sharp) obstructions to symplectic embeddings. These capacities are defined using embedded contact homology, and establishing their basic properties currently requires Seiberg-Witten theory. In this note we define a new sequence of symplectic capacities in four dimensions using only basic notions of holomorphic curves. The new capacities satisfy the same basic properties as ECH capacities and agree with the ECH capacities for the main examples for which the latter have been computed, namely convex and concave toric domains. The new capacities are also useful for obstructing symplectic embeddings into closed symplectic four-manifolds. This work is inspired by a recent preprint of McDuff-Siegel giving a similar elementary alternative to symplectic capacities from rational SFT.
