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arXiv · 1510.02530

Deformations of Lie groupoids

Marius Crainic·João Nuno Mestre·Ivan Struchiner
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Abstract

We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamental properties of the deformation cohomology including Morita invariance, a van Est theorem, and a vanishing result in the proper case. Combined with Moser's deformation arguments for groupoids, we obtain several rigidity and normal form results.

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Marius Crainic, João Nuno Mestre, Ivan Struchiner. 2020-11-17. Deformations of Lie groupoids. https://doi.org/10.1093/imrn%2Frny221

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