Deformations of Lie groupoids
Differential Geometry
2020-11-19 v3
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.
Cite
@article{arxiv.1510.02530,
title = {Deformations of Lie groupoids},
author = {Marius Crainic and João Nuno Mestre and Ivan Struchiner},
journal= {arXiv preprint arXiv:1510.02530},
year = {2020}
}
Comments
45 pages. Published version; corrected typos