Relative Deligne cohomology and Cheeger-Simons characters
Differential Geometry
2014-01-06 v1 Algebraic Topology
Abstract
In the paper [1] (arXiv:math/0408333) 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.
Keywords
Cite
@article{arxiv.1401.0631,
title = {Relative Deligne cohomology and Cheeger-Simons characters},
author = {Fabio Ferrari Ruffino},
journal= {arXiv preprint arXiv:1401.0631},
year = {2014}
}
Comments
16 pages, to appear in Communications in Analysis and Geometry