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 $\tau$ 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 $P_{\tau }$ is the total space of the principal $\mathbb{C}{P}^{\infty }$-bundle induced over X by $\tau$ and ${\hat{K}}_{\ast }$ is obtained form the action of $\mathbb{C}{P}^{\infty }$ on K-theory.

References in corpus (1)

• Units of ring spectra and Thom spectra

Cited by in corpus (6)

• Twisted Morava K-theory and E-theory
• Motivic twisted K-theory
• Twisted Morava K-theory and connective covers of Lie groups
• Twisted differential KO-theory
• A new approach to twisted K-theory of compact Lie groups
• Computations in higher twisted $K$-theory