Integrability of Jacobi and Poisson structures
Annales de l'Institut Fourier, Volume 57 (2007) no. 4, pp. 1181-1216.

We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the prequantization of symplectic groupoids, which answers a question posed by Weinstein and Xu. The methods used are those of Crainic-Fernandes on A-paths and monodromy group(oid)s of algebroids. In particular, most of the results we obtain are valid also in the non-integrable case.

Nous discutons l’intégrabilité des variétés de Jacobi par des groupoïdes de contact. Nous considérons ensuite ce que le point de vue des structures de Jacobi apporte à la géométrie de Poisson. En particulier, en utilisant les groupoïdes de contacts, nous prouvons un théorème à la Kostant sur la préquantization des groupoïdes symplectiques. Ce théorème répond à une question posée par Weinstein et Xu. Nous utilisons les méthodes de Crainic-Fernandes sur les A-paths et les group(oïd)es de monodromie d’algebroïdes. En particulier, la plupart des résultats que nous obtenons sont valides dans le cas non-intégrable.

DOI: 10.5802/aif.2291
Classification: 53D17
Keywords: Jacobi structure, Poisson geometry, prequantization, contact groupoids, integration
Crainic, Marius 1; Zhu, Chenchang 2

1 Utrecht University Department of Mathematics 3508 TA Utrecht (The Netherlands)
2 University of California Department of Mathematics Berkeley, CA 94720 (U.S.A.)
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Crainic, Marius; Zhu, Chenchang. Integrability of Jacobi and Poisson structures. Annales de l'Institut Fourier, Volume 57 (2007) no. 4, pp. 1181-1216. doi : 10.5802/aif.2291. http://www.numdam.org/articles/10.5802/aif.2291/

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