2005/04/13 by Aristide Tsemo, Tsemo Aristide, Aristide, Tsemo
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #math.DG
paper · pdf · doi:10.48550/arxiv.math/0504274
42 pages, 21 references
arxiv created 2005/04/13 · openalex publication_date 2005/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (F,u)→ P→ N be a symplectic fibration in math.SG/0503268 McDuff has defined a subgroup Hams(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 Hams 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