论文标题
Haefliger的可区分共同体学
Haefliger's differentiable cohomology
论文作者
论文摘要
我们回顾了Haefliger的可区分共同体，以$ \ Mathbb {r}^Q $的差异性伪造。我们研究了定义这种同胞所需的结构，该结构与PDE几何研究的基础所谓的Cartan分布相关。我们定义了Haefliger可区分共同体的类似物，用于平坦的cartan群，研究其无穷小的对应物，并通过类似货车的图形将两者相关联。最后，我们定义了与平坦cartan群相关的歧管$ m $上的几何结构的特征图。该结果概括了现有的叶子特征类别的方法。
We review Haefliger's differentiable cohomology for the pseudogroup of diffeomorphisms of $\mathbb{R}^q$. We investigate the structure needed to define such a cohomology, which, remarkably, is related to the so called Cartan distribution underlying the geometric study of PDE. We define an analogue of Haefliger differentiable cohomology for flat Cartan groupoids, investigate its infinitesimal counterpart and relate the two by a Van Est-like map. Finally, we define a characteristic map for geometric structures on manifolds $M$ associated to flat Cartan groupoids. The outcome generalizes the existing approaches to characteristic classes for foliations.
