Twisted K-theory constructions in the case of a decomposable Dixmier–Douady class II: Topological and equivariant models

Abstract

bstract This is a study of twisted K-theory on a product space TˆM . The twisting comes from a decomposable cup product class which applies the 1-cohomology of T and the 2-cohomology of M . In the case of a topological product, we give a concrete realization for the gerbe associated to a cup product characteristic class and use this to realize twisted K 1 -theory elements in terms of supercharge sections in a Fredholm bundle. The nontriviality of this construction is proved. Equivariant twisted K-theory and gerbes are studied in the product case as well. This part applies Lie groupoid theory. Superconnection formalism is used to provide a construction for characteristic polynomials which are used to extract information from the twisted K-theory classes.MSC: 19L50, 53C08, 22A22.

Twisted differential cohomology

“…For a detailed description of the phyiscal motivation we refer to [DFM11]. Twisted complex K-theory and its differential version have been investigated to some extent [DK70], [TXLG04], [AS06], [AS04], [FHT13], [FHT11a], [FHT11b], [BV13], [BCM + 02], [Gom13], [Har12], [MP07], [HM12] (we refrain from listing paper dealing with non-twisted differential K-theory).…”