A manifold structure for the group of orbifold diffeomorphisms of a smooth orbifold

2006/08/21 by Joseph E. Borzellino, Borzellino, Joseph E., Victor Brunsden +1
Mathematics · #22E65 (Secondary) #22F50 #54H99 (Primary) #57S05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:22E65 #msc:22F50 #msc:54H99 #msc:57S05

paper · pdf · doi:10.48550/arxiv.math/0608526

26 pages, 2 figures, final version

openalex publication_date 2006/08/21 · arxiv created 2009/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a compact, smooth C^r orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for finite r ≥ 1 and a Frechet manifold if r=infty. In each case, the local model is the separable Banach (Frechet) space of C^r (Cⁱnfty, resp.) orbisections of the tangent orbibundle.

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