We introduce a type of surgery decomposition of Weinstein manifolds that we call simplicial decompositions. The main result of this paper is that the Chekanov–Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a descent (cosheaf) property with respect to a simplicial decomposition. Simplicial decompositions generalize the notion of Weinstein connected sum and we show that there is a one-to-one correspondence (up to Weinstein homotopy) between simplicial decompositions and so-called good sectorial covers. As an application, we explicitly compute the Chekanov–Eliashberg dg-algebra of the Legendrian attaching spheres of a plumbing of copies of cotangent bundles of spheres of dimension at least three according to any plumbing quiver. We show by explicit computation that this Chekanov–Eliashberg dg-algebra is quasi-isomorphic to the Ginzburg dg-algebra of the plumbing quiver.

中文翻译：

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Chekanov–Eliashberg dg-代数的单纯下降

我们介绍一种 Weinstein 流形的手术分解，我们称之为单纯分解. 本文的主要结果是 Weinstein 流形的附加球体的 Chekanov–Eliashberg dg-代数满足关于单纯分解的下降（cosheaf）性质。单纯分解推广了 Weinstein 连通和的概念，我们证明了单纯分解与所谓的良好扇形覆盖之间存在一对一的对应关系（直至 Weinstein 同伦）。作为一个应用程序，我们明确地计算了根据任何管道箭袋，维数至少为三的余切球体的副本的管道的 Legendrian 附加球体的 Chekanov–Eliashberg dg-代数。我们通过显式计算表明，这个 Chekanov–Eliashberg dg-代数与管道箭筒的 Ginzburg dg-代数是拟同构的。