Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

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.

Publication Year

2014

Journal Title

Journal of the Australian Mathematical Society

Volume number

99

Publisher

Cambridge University Press

First Page (page number)

30

Last Page (page number)

47

Referreed

1

DOI

10.1017/S1446788714000627

ISSN (print)

14467887

ISSN (electronic)

14468107

Link to Publisher’s Edition

http://dx.doi.org/10.1017/S1446788714000627

Copyright

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.

Keywords

primary 53C08, secondary 57R20, 19L50

Included in

Mathematics Commons

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