Relative differential K-characters

TL;DR

This paper introduces a new group of relative differential K-characters linked to smooth maps between compact manifolds, extending existing theories and expressing secondary geometric invariants within this framework.

Contribution

It defines the relative differential K-characters and demonstrates their structure via a short exact sequence, expanding the understanding of secondary geometric invariants.

Findings

The group fits into a short exact sequence similar to the non-relative case.

Secondary geometric invariants are expressed in this new framework.

The theory generalizes existing differential K-theory concepts.

Abstract

We define a group of relative differential K-characters associated with a smooth map between two smooth compact manifolds. We show that this group fits into a short exact sequence as in the non-relative case. Some secondary geometric invariants are expressed in this theory.