We study the top-degree cohomology for the \({\bar{\partial }_b}\) operator defined on a generic submanifold of the complex space as well as for the differential complex associated with a locally integrable structure \({\mathcal {V}}\) over a smooth manifold. The main assumptions are that \({\mathcal {V}}\) is hypocomplex and that the differential complex is locally solvable in degree one. One of the main tools is an adaptation of a sheaf theoretical argument due to Ramis–Ruget–Verdier.

中文翻译：

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CR和局部可整合的超复杂结构中的顶级全局可解性

我们研究了\（{\ bar {\ partial} _b} \）运算符的最高同调性，该运算符定义在复杂空间的一般子流形上以及与局部可积结构\（{\ mathcal {V}} \）在光滑的流形上。主要假设是\（{\ mathcal {V}} \）是低复数，而微分复数在一级中是局部可解的。主要工具之一是对Ramis–Ruget–Verdier的捆理论论证的改编。