AI 中文总结
本文研究闭辛曲面上预量子化圆丛的嵌入接触同调的U-模结构，给出U-映射显式描述，计算ECH谱及辛除子补集的ECH容量，证明闭积分辛流形的ECH容量无穷。
AI 中文摘要
本文旨在研究闭辛曲面上一类预量子化圆丛的嵌入接触同调（ECH）的U-模结构，假设每个圆丛的欧拉数严格小于对应曲面的欧拉示性数。我们通过配边映射定义的滤过ECH的基，给出了U-映射的显式描述；利用该U-映射公式计算ECH谱，并将其作为应用，计算辛除子的某些补集的ECH容量。此外，我们证明闭积分辛流形的ECH容量是无穷的。
英文摘要
The purpose of this paper is to study the $U$-module structure of the embedded contact homology of a class of prequantization circle bundles over closed symplectic surfaces. We assume that the Euler number of each circle bundle is strictly less than the Euler characteristic of the corresponding surface. We give an explicit description of the $U$-map with respect to a basis of filtered ECH defined via cobordism maps. We use the formula for the $U$-map to compute the ECH spectrum and, as an application, the ECH capacities of certain complements of symplectic divisors. Furthermore, we show that the ECH capacities of closed integral symplectic manifolds are infinite.
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