Relative differential characters

TL;DR

This paper compares two natural approaches to defining relative Cheeger-Simons differential characters, relating their constructions and clarifying their connections within differential geometry.

Contribution

It analyzes and relates two different constructions of relative Cheeger-Simons differential characters, extending prior work by Cheeger, Simons, Hopkins, and Singer.

Findings

Both approaches are compatible and can be related through a detailed comparison.

The paper clarifies the relationship between the two definitions of relative differential characters.

It provides a unified perspective on the construction of relative Cheeger-Simons groups.

Abstract

There are two natural candidates for the group of relative Cheeger-Simons differential characters. The first directly extends the work of Cheeger and Simons and the second extends the description given by Hopkins and Singer of the Cheeger-Simons group as the homology of a certain cochain complex. We discuss both approaches and relate the two relative groups.