A universal coefficient theorem for twisted K-theory

Abstract

In this paper, we recall the definition of twisted K-theory in various settings. We prove that for a twist $τ$ corresponding to a three dimensional integral cohomology class of a space X, there exist a "universal coefficient" isomorphism K_{*}^τ(X)\cong K_{*}(P_τ)\otimes_{K_{*}(\mathbb{C}P^{\infty})} \hat{K}_{*} where $P_τ$ is the total space of the principal $\mathbb{C}P^{\infty}$-bundle induced over X by $τ$ and $\hat K_*$ is obtained form the action of $\mathbb{C}P^{\infty}$ on K-theory.