Compactly-supported and relative integration in differential cohomology

Abstract

In this work, we have constructed more general versions of differential integration maps in differential cohomology theories. Among the obtained versions we can mention the integration with compact supports, the integration with vertically compact supports and their relative versions. To obtain these maps, it was necessary to construct a special product between parallel and relative differential classes and to extend differential cohomology theories to a category of sequences of manifolds.