Relative Deligne cohomology and Cheeger-Simons characters

In [1] 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 [1]. Finally, we show how the explicit formulas for the holonomy, the transgression maps and the integration can be extended to the relative case.

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Published 2 July 2014