Geodesic
Integrability of Lie brackets
Marius Crainic1 ; Rui Loja Fernandes2
1 Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720, United States and Mathematical Institute, Utrecht University, NL-3508 TA Utrecht, The Netherlands
2 Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
Annals of mathematics, Tome 157 (2003) no. 2, pp. 575-620

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.

DOI : 10.4007/annals.2003.157.575

Marius Crainic 1 ; Rui Loja Fernandes 2

1 Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720, United States and Mathematical Institute, Utrecht University, NL-3508 TA Utrecht, The Netherlands
2 Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal 
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Marius Crainic; Rui Loja Fernandes. Integrability of Lie brackets. Annals of mathematics, Tome 157 (2003) no. 2, pp. 575-620. doi: 10.4007/annals.2003.157.575

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