论文标题
奇异riemannian叶的基本同谋
Equivariant basic cohomology of singular Riemannian foliations
论文作者
论文摘要
我们介绍了具有横向无穷小动作的单数riemannian叶子的模棱两可的基本共同体的概念，并证明了某些基本特性，例如其在同型下的不变性。对于奇异杀戮叶子的特殊情况，其结构代数的自然横向作用。我们证明，莫德洛扭转，其均等基本的同一个同谋本地化在叶子的封闭叶子的集合中，本着古典本地化定理的精神。作为应用，我们获得了基本的Euler特征也定位在该集合中，并且局部叶面的基本同胞的维度小于或等于整个叶片的尺寸，而相等性则是在均值正式的情况下。
We introduce the notion of equivariant basic cohomology for singular Riemannian foliations with transverse infinitesimal actions, and prove some elementary properties such as its invariance under homotopies. For the particular case of singular Killing foliations, there is the natural transverse action of its structural algebra. We prove that, modulo torsion, its equivariant basic cohomology localizes to the set of closed leaves of the foliation, in the spirit of the classical localization theorem of Borel. As applications, we obtain that the basic Euler characteristic also localizes to this set, and that the dimension of the basic cohomology of the localized foliation is less than or equal to that of the whole foliation, with equality occurring precisely in the equivariantly formal case.
