Integrability of Lie brackets

• 成果类型: Article
• 署名作者: Crainic, M; Fernandes, RL
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2003.157.575
• 发表日期: 2003
• 页码: 575-620
• 关键词: integration; algebroids; groupoids; holonomy

摘要

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.