Communications in Analysis and Geometry
Volume 22 (2014)
Relative Deligne cohomology and Cheeger-Simons characters
Pages: 573 – 593
In  the authors discuss two possible definitions of the relative Cheeger-Simons characters, the second one fitting into a long exact sequence. Here we relate that picture to the one of the relative Deligne cohomology groups, defined via the mapping cone: we show that there are three meaningful relative groups, and we analyze the corresponding definition of relative Cheeger-Simons characters in each case.We then extract another definition, corresponding to the one fitting into a long exact sequence in . Finally, we show how the explicit formulas for the holonomy, the transgression maps and the integration can be extended to the relative case.