论文标题
叶叶转向椭圆形操作员的索引
The index of leafwise G-transversally elliptic operators on foliations
论文作者
论文摘要
我们在光滑的封闭的叶状歧管上介绍和研究G不变的叶轮G-转换椭圆形算子，并具有紧凑型组G的叶轮作用。在自由动作的情况下，我们将索引类别与商叶片上相应的叶轮椭圆算子的Connes-skandalis索引类联系起来。最后，我们证明了我们的索引形态与Gysin Thom同构的兼容性，并将其计算减少到Tori作用的情况下。我们还使用Kasparov Dirac元素来构建索引定理的拓扑候选者，用于欧几里得G代表。
We introduce and study the index morphism for G-invariant leafwise G-transversally elliptic operators on smooth closed foliated manifolds which are endowed with leafwise actions of the compact group G. We prove the usual axioms of excision, multiplicativity and induction for closed subgroups. In the case of free actions, we relate our index class with the Connes-Skandalis index class of the corresponding leafwise elliptic operator on the quotient foliation. Finally we prove the compatibility of our index morphism with the Gysin Thom isomorphism and reduce its computation to the case of tori actions. We also construct a topological candidate for an index theorem using the Kasparov Dirac element for euclidean G-representations.
