Integration of closed forms in diffeology
December 31, 2013, update December 31, 2013

This is a work in progress, a first announce. For any comment  send me an
WORK IN PROGRESS. — I explore a geometrical representation of De Rham cohomology classes, for closed 1 and 2-forms, on diffeological spaces. In particular a closed 2-form is always the curvature of a connection on a principal bundle with group its torus of periods, when its group of periods is diffeologically discrete. This condition is satisfied by any differential forms defined on Hausdorff second-countable manifolds. Therefore, on manifolds: Every closed 2-form is the curvature of a connection. I give also a classification of these integration structures in terms of representations of the fundamental group.