论文标题
类似于Orbifold且适当的$ \ Mathfrak G $ -Manifolds
Orbifold-like and proper $\mathfrak g$-manifolds
论文作者
论文摘要
在[4]和[5]中，我们将完成无限的群体动作$ζ的完成概念概念：{\ mathfrak g} \ to \ mathfrak x（m）$ to \ mathfrak x（m）$ to在（非compact）歧管$ m $上进行的实际组动作，最初是由R. Palais [9]介绍的，并通过示例显示了一个feaforperies fore propation propation properiation for profial propories for for for for for for for a for for a for a for。在本文中，我们介绍并调查了$ \ mathfrak g $ -Manifolds的Tamer类，称为Orbifold（类似于Orbifold），为此，完成该类别具有Orbifold结构。这类$ \ mathfrak g $ -manifolds在其本地拓扑结构方面相当良好，以使许多几何结构变得有意义。特别是，我们研究了适当的$ \ mathfrak g $ actions，并将适当的小组操作的许多常用属性概括为更一般的环境。
In [4] and [5], we generalized the concept of completion of an infinitesimal group action $ζ: {\mathfrak g} \to \mathfrak X (M)$ to an actual group action on a (non-compact) manifold $M$, originally introduced by R. Palais [9], and showed by examples that this completion may have quite pathological properties (much like the leaf space of a foliation). In the present paper, we introduce and investigate a tamer class of $\mathfrak g$-manifolds, called orbifold--like, for which the completion has an orbifold structure. This class of $\mathfrak g$-manifolds is reasonably well-behaved with respect to its local topological and smooth structure to allow for many geometric constructions to make sense. In particular, we investigate proper $\mathfrak g$-actions and generalize many of the usual properties of proper group actions to this more general setting.
