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
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Link to Publisher’s Edition
This article has been published in a revised form in Journal of the Australian Mathematical Society http://dx.doi.org/10.1017/S1446788714000627. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2014 Australian Mathematical Publishing Association Inc.
primary 53C08, secondary 57R20, 19L50
Ho, Man Ho. "On differential characteristic classes." Journal of the Australian Mathematical Society 99 (2014): 30-47.