We show that moduli spaces of transversely cut-out (perturbed) pseudo-holomorphic curves in an almost complex manifold carry canonical relative smooth structures (“relative to the moduli space of domain curves”). The main point is that these structures can be characterized by a universal property. The tools required are ordinary gluing analysis combined with some fundamental results from the polyfold theory of Hofer–Wysocki–Zehnder.

中文翻译：

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Gromov–Witten 模空间上的 Rel–$C^\infty$ 结构

我们表明，在几乎复杂的流形中，横向切出（扰动）伪全纯曲线的模空间携带规范的相对平滑结构（“相对于域曲线的模空间”）。主要的一点是，这些结构可以用一个通用属性来表征。所需的工具是普通的胶合分析，结合 Hofer-Wysocki-Zehnder 的多折叠理论的一些基本结果。