Weinstein, Alan Linearization of regular proper groupoids. (English) Zbl 1043.58009 J. Inst. Math. Jussieu 1, No. 3, 493-511 (2002). The author hopes eventually to establish a linearization theorem for all proper groupoids near their orbits, as was expressed in [A. Weinstein, Lett. Math. Phys. 52, No. 1, 93–102 (2000; Zbl 0961.22004)]. Since the most general version would require a still unproven linearization theorem around fixed points, this paper is devoted to a proof of a somewhat restricted theorem claiming that, under a differential-topological finiteness assumption, the Lie groupoid is isomorphic to its linear approximation in some neighborhood of each orbit. The theorem follows from a slice theorem asserting that a linearization of the restriction to a slice extends to a linearization along an orbit. Reviewer: Hirokazu Nishimura (Tsukuba) Cited in 1 ReviewCited in 30 Documents MSC: 58H05 Pseudogroups and differentiable groupoids 57R99 Differential topology Keywords:Lie groupoid; proper action; submersion Citations:Zbl 0961.22004 PDFBibTeX XMLCite \textit{A. Weinstein}, J. Inst. Math. Jussieu 1, No. 3, 493--511 (2002; Zbl 1043.58009) Full Text: DOI arXiv