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ON DIFFERENTIAL CHARACTERISTIC CLASSES

Part of: Differential topology Topological $K$-theory Global differential geometry

Published online by Cambridge University Press:  04 December 2014

MAN-HO HO
MAN-HO HO*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong email [email protected]
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Abstract

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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.

Keywords

characteristic classesdifferential charactersdifferential K-theory

MSC classification

Primary: 53C08: Gerbes, differential characters
Secondary: 57R20: Characteristic classes and numbers 19L50: Twisted $K$-theory; differential $K$-theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 1 , August 2015 , pp. 30 - 47
Copyright
© 2014 Australian Mathematical Publishing Association Inc. 

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