论文标题
等距谎言对riemannian群的2组作用
Isometric Lie 2-group actions on Riemannian groupoids
论文作者
论文摘要
我们通过表现出一些直接的属性和含义来研究Riemannian Groupoid的谎言$ 2 $组的等轴测动作。首先，我们证明了存在的结果，该结果允许获得Slice定理的2个等级版本和Equivariant管状邻域定理，并在紧凑型Lie 2 $ group上构建双不景气的groupoid指标。我们提供自然的例子，转移一些经典的结构，并解释这种等距$ 2 $ -ACTION的概念如何产生一种开发关于lie groupoids的2级莫尔斯理论的方法。其次，我们对等距谎言$ 2 $ - 组动作进行无限描述。我们定义了与lieemanian liemantoid上任何与任何riemannian $ n $ metric相关的横向无限同量代数的代数，这又引起了商人堆栈上的几何杀死矢量场的概念。如果我们的Riemannian堆栈分开，那么我们证明由这种几何杀伤矢量场形成的代数始终是有限的。
We study isometric actions of Lie $2$-groups on Riemannian groupoids by exhibiting some of their immediate properties and implications. Firstly, we prove an existence result which allows both to obtain 2-equivariant versions of the Slice Theorem and the Equivariant Tubular Neighborhood Theorem and to construct bi-invariant groupoid metrics on compact Lie $2$-groups. We provide natural examples, transfer some classical constructions and explain how this notion of isometric $2$-action yields a way to develop a 2-equivariant Morse theory on Lie groupoids. Secondly, we give an infinitesimal description of an isometric Lie $2$-group action. We define an algebra of transversal infinitesimal isometries associated to any Riemannian $n$-metric on a Lie groupoid which in turn gives rise to a notion of geometric Killing vector field on a quotient Riemannian stack. If our Riemannian stack is separated then we prove that the algebra formed by such geometric Killing vector fields is always finite dimensional.
