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Linearization of regular proper groupoids. (English) Zbl 1043.58009

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.

MSC:

58H05 Pseudogroups and differentiable groupoids
57R99 Differential topology

Citations:

Zbl 0961.22004
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