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Integrability of Jacobi and Poisson structures. (English) Zbl 1146.53055

Summary: 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 A. Weinstein and P. Xu [J. Reine Angew. Math. 417, 159–189 (1991; Zbl 0722.58021)]. 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.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids

Citations:

Zbl 0722.58021

References:

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