Integration of Coupling Dirac Structures
arXiv:1409.7899 · doi:10.2140/pjm.2015.278.325
Abstract
Coupling Dirac structures are Dirac structures defined on the total space of a fibration, generalizing hamiltonian fibrations from symplectic geometry, where one replaces the symplectic structure on the fibers by a Poisson structure. We study the associated Poisson gauge theory, in order to describe the presymplectic groupoid integrating coupling Dirac structures. We find the obstructions to integrability and we give explicit geometric descriptions of the integration.
48 pages, Final version accepted for publication in Pacific Journal of Mathematics