Integrability of Jacobi structures

Details Integrability of Jacobi structures Integrability of Jacobi structures

2004-03-16

arxiv.org/abs/math/0403268v1

Ann. Inst. Fourier (Grenoble) 57 (2007), no. 4, 1181--1216.

Mathematics

Differential Geometry

25 pages

Scientific paper

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 \cite{prequan}. 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.

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