Given a contact manifold $M_#$ together with a transversal infinitesimalautomorphism $\xi$, we show that any local leaf space $M$ for the foliationdetermined by $\xi$ naturally carries a conformally symplectic (cs-) structure.Then we show that the Rumin complex on $M_#$ descends to a complex ofdifferential operators on $M$, whose cohomology can be computed. Applying thisconstruction locally, one obtains a complex intrinsically associated to anymanifold endowed with a cs-structure, which recovers the generalization of theso-called Rumin-Seshadri complex to the conformally symplectic setting. Thecohomology of this more general complex can be computed using the push-downconstruction.
展开▼
机译：给定一个接触流形$ M _＃$以及一个横向无限小自同构$ \ xi $，我们证明了由$ \ xi $所确定的叶子的任何局部叶空间$ M $自然都带有保形辛（cs-）结构。 $ M _＃$上的Rumin复数下降为$ M $上的微分算子复数，可以计算其同调性。局部地应用这种构造，可以获得与赋予cs结构的任何流形固有相关的复合物，这将所谓的Rumin-Seshadri复合物恢复到共形辛环境。可以使用下推式构造来计算这种更一般的复合体的同调性。
展开▼
