Some Connections Between Bunke-Schick Differential K-theory and Topological $\mathbb{Z}/k\mathbb{Z}$ K-theory

Abstract

The purpose of this note is to prove some results in Bunke-Schick differential K-theory and topological $\mathbb{Z}/k\mathbb{Z}$ K-theory. The first one is an index theorem for the odd-dimensional geometric families of $\mathbb{Z}/k\mathbb{Z}$-manifolds. The second one is an alternative proof of the Freed-Melrose $\mathbb{Z}/k\mathbb{Z}$-index theorem in the framework of differential K-theory.