Integrability of Lie brackets


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 controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrability by local Lie groupoids, we clarify the smoothness of the Poisson sigma-model for Poisson manifolds, and we describe other geometrical applications.


Marius Crainic

Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720, United States and Mathematical Institute, Utrecht University, NL-3508 TA Utrecht, The Netherlands

Rui Loja Fernandes

Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal