与通用闭合二形式相关的分层以及分层 $L_\infty$ 空间
Stratifications associated to generic closed two-forms and stratified $L_\infty$ spaces
AI总结：
本文研究了通用闭合二形式与分层 $L_\infty$ 空间的关系，通过构造分层结构和关联 $L_\infty$ 空间来扩展对 $L_\infty$ 结构的研究。
摘要：
Jae-Suk Park 和第二作者将共isorsubmanifolds 在 symplectic manifold 上的变形问题定义为研究与对应 presymplectic 结构的 null foliation 关联的 foliation de-Rham 复合体的 Mauer-Cartan 模型问题的 $L_\infty$ 代数。本文的主要目的是将对 $L_\infty$ 结构的研究扩展到任意光滑流形上通用闭合二形式的情况，作为分层 $L_\infty$ 空间。我们首先证明存在一个余集的闭合 2 形式，我们称之为 $Z^2_{reg}(M) \subset Z^2(M)$，使得任取其中的元素 $ω$ 都可以接受一个 Whitney 分层，每个分层都是 presymplectic manifold。然后我们为每个分层（及其管状邻域）关联一个 $L_\infty$ 空间，并通过由 $L_\infty$ morphisms 组成的坐标 atlas 将这些 $L_\infty$ 空间粘合为一个全局的分层 $L_\infty$ 空间，其中这些 $L_\infty$ morphisms 不一定是 quasi-isomorphisms。
英文摘要：
Jae-Suk Park and the second-named author introduce the deformation problem of coisotropic submanifolds of a symplectic manifold as the study of Mauer-Cartan moduli problem of an $L_\infty$ algebra attached to the foliation de-Rham complex associated to the null foliation of the corresponding presymplectic structure. The main purpose of the present paper is to extend this study of $L_\infty$ structures to the case of generic closed two-forms on arbitrary smooth manifolds as a stratified $L_\infty$ space. We first prove that there exists a residual subset of closed 2-forms, which we denote by $Z^2_{reg}(M) \subset Z^2(M)$, such that any element $ω$ therefrom admits a Whitney stratification each of whose strata is a presymplectic manifold. We then associate an $L_\infty$ space to each stratum (and to its tubular neighborhood) and glue the collection of $L_\infty$ spaces to a global stratified $L_\infty$ space by the coordinate atlas consisting of $L_\infty$ morphisms, which is a collection of $L_\infty$ morphisms, not necessarily of quasi-isomorphisms.
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