In this paper we give explicit formulas for differential characteristic classes of principal G-bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin classes and the differential Euler class. Furthermore, we show that the differential Chern class is the unique natural transformation from (Simons-Sullivan) differential K-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 K-theory. Finally, we discuss the odd differential Chern classes.
|Number of pages||18|
|Journal||Journal of the Australian Mathematical Society|
|Publication status||Published - 24 Aug 2015|
Scopus Subject Areas
- characteristic classes
- differential characters
- differential K-theory