Integration of simplicial forms and Deligne cohomology - Dupont, Johan L.; Ljungmann, Rune (MATHEMATICA SCANDINAVICA, 2005)
We present two approaches to constructing an integration map along the fiber for smooth Deligne cohomology. The first is defined in the simplicial model, where a class in Deligne cohomology is represented by a simplicial form, and the second in a related but more combinatorial model .