Twisted K-theory

Summary

Twisted K-theory is a variant of complex K-theory of a space $X$ that depends on an extra datum, a twist. Twists are classified by classes in $H^3(X; \Z)$. With the trivial twist it is ordinary K-theory. It arises from bundles of Fredholm operators glued with projective unitary transformations. It appears in string theory, in the representation theory of loop groups and in the study of continuous-trace C*-algebras.