82 citations · 141 across the 6 of their papers we have counts for
10 papers · 1 filter
Rigidity and Flexibility in Poisson Geometry
Rui Loja Fernandes, Marius Crainic
We discuss several rigidity and flexibility phenomena in the context of Poisson geometry.
Generalized complex structures and Lie brackets
Marius Crainic
We look at generalized complex structures from the point of view of Poisson and Dirac geometry and we remark that the puzzling equations underlying the notion of generalized comple…
Prequantization and Lie brackets
Marius Crainic
We start by describing the relationship between the classical prequantization condition and the integrability of a certain Lie algebroid associated to the problem and use this to g…
Deformations of Lie brackets: cohomological aspects
M. Crainic, I. Moerdijk
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algeb…
Integrability of Poisson brackets
Marius Crainic, Rui Loja Fernandes
We show that various notions of integrability for Poisson brackets are all equivalent, and we give the precise obstructions to integrating Poisson manifolds. We describe the integr…
Integrability of Lie brackets
Marius Crainic, Rui L. Fernandes
In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controll…