Integration of conformal Jacobi fibrations and prequantization of Poisson fibrations (Q380771)

The author introduces conformal Jacobi fibrations, which unify Poisson and contact fiber bundles, and discusses the integration problems involved. By a conformal Jacobi fibration is meant a locally trivial fiber bundle \(p:M\rightarrow B\), where \(M\) and \(B\) are manifolds whose fiber type \(F\) is a Jacobi manifold together with a set of trivializations, whose transition maps preserve the conformal class of the Jacobi structure of \(F\). The author further examines some applications of this theory to the prequantization of Poisson fibrations and shows that the simply connected symplectic groupoid associated to a prequantizable and integrable Poisson fibration is also prequantizable. This is a nice result.