Motivated by the study of symplectic Lie algebroids, we focus on a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to the study of singular differential forms and their cohomology. This setting generalizes $b$-symplectic manifolds, foliated manifolds, and a wide class of Poisson manifolds. We generalize Moser’s theorem to this setting, and use it to construct symplectomorphisms between singular symplectic forms. We give applications of this machinery (including the study of Poisson cohomology), and study specific examples of a few of them in depth.

中文翻译：

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$ E $流形的几何

在辛李代数的研究的推动下，我们专注于一种类型的代数（称为E $切线束），该代数特别适合于奇异微分形式及其同调性的研究。此设置概括了$ b $的渐进形流形，叶形流形和一类广泛的Poisson流形。我们将Moser定理推广到此设置，并使用它来构造奇异辛形式之间的辛同构。我们给出了这种机械的应用（包括对泊松同调的研究），并深入研究了其中一些的具体示例。