Deformations of Lie Groupoids

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Author(s):	Crainic, Marius ^[1] ; Mestre, Joao Nuno ^[1] ; Struchiner, Ivan ^[2] Total Authors: 3
Affiliation:	^[1] Univ Utrecht, Dept Math, NL-3508 TA Utrecht - Netherlands ^[2] Univ Sao Paulo, Dept Math, Sao Paulo - Brazil Total Affiliations: 2
Document type:	Journal article
Source:	INTERNATIONAL MATHEMATICS RESEARCH NOTICES; v. 2020, n. 21, p. 7662-7746, NOV 2020.
Web of Science Citations:	2
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. (AU)

FAPESP's process:	13/16753-8 - Stability of Lie brackets and their morphisms
Grantee:	Ivan Struchiner
Support Opportunities:	Regular Research Grants