Department of Mathematics
In this paper we give explicit formulas of dierential characteristic classes of principal G-bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, dierential Pontryagin classes and dierential Euler class. Furthermore, we show that the dierential Chern class is the unique natural transformation from (Simons-Sullivan) dierential K-theory to (Cheeger-Simons) dierential characters that is compatible with curvature and characteristic class. We also give the explicit formula for the dierential Chern class on Freed-Lott dierential K-theory. Finally we discuss the odd dierential Chern classes.
Journal of the Australian Mathematical Society
Cambridge University Press
First Page (page number)
Last Page (page number)
Ho, Man Ho. "On differential characteristic classes." Journal of the Australian Mathematical Society 99 (2014): 30-47.