论文标题
K理论和索引理论对流形，具有适当的谎言小组行动
K-theory and index theory on manifolds with a proper Lie group action
论文作者
论文摘要
该论文专门介绍了具有适当的谎言组作用的轨道和横向椭圆算子的索引理论。它纠正了我以前的论文（2016年在JNCG上发表）的错误，并包含新的结果。两种索引理论，轨道和横向是非常相互交织和相互依存的，并被一起处理。轨道运算符的理论是从基本定义到最终索引定理的。在第9、10、11节中给出了用于椭圆，T椭圆和轨道椭圆算子的索引定理的KK理论证明。在整篇论文中，我们在构造伪分化的算子中使用了更简单的方法。
The paper is devoted to the index theory of orbital and transverse elliptic operators on manifolds with a proper Lie group action. It corrects errors of my previous paper (published in JNCG in 2016) on transverse operators and contains new results. The two index theories, orbital and transverse, are very much intertwined and interdependent, and are treated together. The theory of orbital operators is developed from the basic definitions to the final index theorem. The KK-theoretic proofs of index theorems for elliptic, t-elliptic and orbital elliptic operators are given in sections 9, 10, 11. Throughout the paper, we use a simpler method in constructing pseudo-differential operators.
