On the linearization theorem for proper Lie groupoids

By M. Crainic, I. Struchiner. 2011

54 citations recorded by the source corpus.

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).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4759851891892f58d8eb7c9b1e27a3dc337fb738

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Lie groupoids and their orbispaces (2012, unknown): “The proof of this can be consulted in [7].”
Riemannian metrics on Lie groupoids (2014, background): “11 the main results on linearization of proper groupoids that one can find in the literature [6, 16, 19–21]:”