Remarks on flat and differential K-theory

TL;DR

This paper proves compatibility between different topological indices in flat and differential K-theory and establishes explicit isomorphisms between two models of differential K-theory.

Contribution

It provides a direct proof of the compatibility of differential and flat topological indices and constructs explicit isomorphisms between two differential K-theory models.

Findings

Compatibility of differential and flat topological indices established

Explicit isomorphisms between Bunke-Schick and Freed-Lott differential K-theories

Contributions to the understanding of flat and differential K-theory structures

Abstract

In this note we prove some results in flat and differential $K$-theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential $K$-theory and Freed-Lott differential $K$-theory.