Abstract

Twisted K-Theory can be expressed in terms of section algebras of locally trivial bundles of compact operators. However, from the point of view of homotopy theory, this setup just captures a small portion of the possible twists. In joint work with Marius Dadarlat we generalised the classical theory to a C-algebraic model, which captures the higher twists of K-theory as well and is based on strongly self-absorbing C-algebras. In this talk I will discuss possible generalisations to the equivariant case, which is joint work with David Evans. In particular, I will first review the construction of the equivariant twist of U(n) representing the generator of its equivariant third cohomology group with respect to the conjugation action of U(n) on itself. Then I will talk about work in progress on a generalisation to (localised) higher twisted K-theory. 

• A Dixmier-Douady theory for strongly self-absorbing C-algebras arXiv:1302.4468
• Unit spectra of K-theory from strongly self-absorbing C-algebras arXiv:1306.2583