Abstract
We study Cheeger–Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit formula for any natural transformation between a differential cohomology theory and the model given by differential characters. Fiber integration for fibers with boundary is treated in the context of relative differential characters. As applications we treat higher-dimensional holonomy, parallel transport, and transgression.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bär, C., Becker, C. (2014). Differential Characters and Geometric Chains. In: Differential Characters. Lecture Notes in Mathematics, vol 2112. Springer, Cham. https://doi.org/10.1007/978-3-319-07034-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-07034-6_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07033-9
Online ISBN: 978-3-319-07034-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)