On the linearization theorem for proper Lie groupoids

Marius Crainic; Ivan Struchiner

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arXiv · 1103.5245

On the linearization theorem for proper Lie groupoids

Marius Crainic·Ivan Struchiner

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Abstract

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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Marius Crainic, Ivan Struchiner. 2012-10-29. On the linearization theorem for proper Lie groupoids. https://arxiv.org/abs/1103.5245

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