  Let (F,u)\to P\to N be a symplectic fibration in math.SG/0503268 McDuff has
defined a subgroup Ham^s(F,u) of the group of symplectic automorphisms of(F,u).
She has shown that the cohomology class [u] of u can be extended to P if and
only if the symplectic fibration has an Ham^s reduction. To show this result,
she constructs a class who represents the obstruction to extend u. This class
can be identified to a 3-class of P using a spectral sequence. The purpose of
this paper is to define a 2-gerbe whose classifying cocycle is the class
defined by McDuff. To define this 2-gerbe, we construct fundamental gerbes in
Dirac geometry which represents the obstruction of [u] to be exact or integral.
Using this gerbes we propose a quantization of symplectic manifolds

Differential Geometry