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 email.mailto:piz@math.huji.ac.il?subject=About%20%22Integration%20of%20closed%20forms%20in%20diffeology%22shapeimage_2_link_0
 
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.