On Differential Characteristic Classes

Man-Ho Ho*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)
33 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)30-47
Number of pages18
JournalJournal of the Australian Mathematical Society
Issue number1
Early online date4 Dec 2014
Publication statusPublished - Aug 2015

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • characteristic classes
  • differential characters
  • differential K-theory


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