Deformations of Lie groupoids

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.

45 pages. Published version; corrected typos

References in corpus (3)

• Stability and invariants of Hilsum-Skandalis maps
• Riemannian metrics on differentiable stacks
• Morita equivalences of vector bundles

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• Deformations of Linear Lie Brackets
• Multiplicative Connections and Their Lie Theory
• Integrating Nijenhuis Structures
• The general linear 2-groupoid
• Deformations of symplectic groupoids
• Differentiable groupoid objects and their abstract Lie algebroids
• Deformation Cohomology of Lie Algebroids and Morita Equivalence
• On the Lie 2-algebra of sections of an LA-groupoid
• Multiplicative Gray stability
• Higher Vector Bundles