Characterization of differential K-theory by hexagon diagram

TL;DR

This paper proves that differential K-theory is uniquely characterized by a hexagon diagram, establishing its rigidity and a unique realization of -K-theory as flat theory, answering a question by Simons and Sullivan.

Contribution

It demonstrates the uniqueness of differential K-theory via the character diagram and confirms a canonical realization of -K-theory as flat theory.

Findings

Differential K-theory is uniquely determined by the character diagram.

There is a canonical realization of -K-theory as the flat theory.

The results affirm the rigidity of differential K-theory and its structures.

Abstract

Using a canonical topology on differential K-theory induced from the Frech\'et space topology on differential forms and the discrete topology on topological K-theory, we prove that differential K-theory is uniquely determined by the character diagram up to a unique natural equivalence, thus giving an affirmative answer to a question asked by Simons and Sullivan in \cite{SS10}. We further deduce rigidity results including that there is a unique way of realizing $\RR/\ZZ$-K-theory as the flat theory, strengthening the results of \cite{BS10}.