On differential characteristic classes
arXiv:1311.3927 · doi:10.1017/S1446788716000070
Abstract
In this paper we give explicit formulas of differential characteristic classes of principal -bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin classes and differential Euler class. Furthermore, we show that the differential Chern class is the unique natural transformation from (Simons-Sullivan) differential -theory to (Cheeger-Simons) differential characters that is compatible with curvature and characteristic class. We also give the explicit formula for the differential Chern class on Freed-Lott differential -theory. Finally we discuss the odd differential Chern classes.
19 pages. Comments are welcome. Final version. Accepted for publication by Journal of the Australian Mathematical Society