Orbifold-like and proper g\mathfrak g-manifolds

Abstract

In [4] and [5], we generalized the concept of completion of an infinitesimal group action ζ:gX(M)\zeta : {\mathfrak g} \to \mathfrak X (M) to an actual group action on a (non-compact) manifold MM, 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 g\mathfrak g-manifolds, called orbifold--like, for which the completion has an orbifold structure. This class of g\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 g\mathfrak g-actions and generalize many of the usual properties of proper group actions to this more general setting.Comment: 18 page

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