Characterization of differential K-theory by hexagon diagram

Abstract

Using a canonical topology on differential K-theory induced from the Frechét 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}.

Second version strengthens our previous results to that differential K-theory is not only unique but unique up to a unique equivalence; we further show that there is a unique way of realizing R/Z-theory as the flat theory