We study the cohomology of the complexes of differential, integral and a particular class of pseudo-forms on odd symplectic manifolds taking the wedge product with the symplectic form as a differential. We thus extend the result of Ševera and the related results of Khudaverdian–Voronov on interpreting the BV odd Laplacian acting on half-densities on an odd symplectic supermanifold. We show that the cohomology classes are in correspondence with inequivalent Lagrangian submanifolds and that they all define semidensities on them. Further, we introduce new operators that move from one Lagragian submanifold to another and we investigate their relation with the so-called picture changing operators for the de Rham differential. Finally, we prove the isomorphism between the cohomology of the de Rham differential and the cohomology of BV Laplacian in the extended framework of differential, integral and a particular class of pseudo-forms.

我们研究奇异辛流形上的微分，积分和一类特殊形式的伪形式的复同同性，以具有辛形式的楔积作为微分。因此，我们扩展了Ševera的结果以及Khudaverdian-Voronov的相关结果，以解释作用于奇辛超流形上半密度的BV奇拉普拉斯算子。我们证明了同调类与不等价的拉格朗日子流形相对应，并且它们都定义了半密度。此外，我们引入了新的算子，它们从一个Lagragian子流形移动到另一个子流形，并研究了它们与de Rham微分的所谓的图片变换算子的关系。最后，