We introduce tame sc‑Fredholm sections and slices of sc-Fredholm sections. A slice is a notion of subpolyfold that is compatible with the sc‑Fredholm section and has finite locally constant codimension. We prove that the subspace of a tame polyfold that satisfies a transverse sc-smooth constraint in a finite dimensional smooth manifold is a slice of any tame sc‑Fredholm section compatible with the constraint. Moreover, we prove that a sc‑Fredholm section restricted to a slice is a tame sc-Fredholm section with a drop in Fredholm index given by the codimension of the slice. As a corollary, we obtain fiber products of tame sc‑Fredholm sections. We describe applications to Gromov–Witten invariants, constructing the Piunikhin–Salamon–Schwarz maps for general closed symplectic manifolds, and avoiding sphere bubbles in moduli spaces of expected dimension $0$ and $1$.

中文翻译：

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约束模空间的多倍正则化

我们介绍驯服的 sc-Fredholm 部分和 sc-Fredholm 部分的切片。切片是与 sc-Fredholm 截面兼容并具有有限局部常数余维的子多折的概念。我们证明了在有限维光滑流形中满足横向 sc-smooth 约束的驯服多折的子空间是与约束兼容的任何驯服 sc-Fredholm 截面的切片。此外，我们证明了限制到切片的 sc-Fredholm 截面是一个温和的 sc-Fredholm 截面，其中 Fredholm 指数下降，由切片的余维给出。作为推论，我们获得了驯服的 sc-Fredholm 部分的纤维产品。我们描述了 Gromov-Witten 不变量的应用，为一般闭合辛流形构建 Piunikhin-Salamon-Schwarz 映射，