2022/09/30 by Franz W. Kamber, Peter W. Michor, Kamber, Franz W. +1
Mathematics · #22F05 #37C10 #54H15 #57R30 #57S05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2209.15432
openalex publication_date 2022/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [4] and [5], we generalized the concept of completion of an infinitesimal group action ζ: \mathfrak g → \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.