On the linearization theorem for proper Lie groupoids

Details On the linearization theorem for proper Lie groupoids On the linearization theorem for proper Lie groupoids

2011-03-27

arxiv.org/abs/1103.5245v1

Mathematics

Differential Geometry

18 pages

Scientific paper

We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passing to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise conditions needed for the theorem to hold (which often have been misstated in the literature).

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