# nLab twisted differential K-theory

### Context

#### Differential cohomology

differential cohomology

## Ingredients

• cohomology

• differential geometry

• ## Connections on bundles

• connection on a bundle

• curvature

• Chern-Weil theory

• ## Higher abelian differential cohomology

• differential function complex

• differential orientation

• ordinary differential cohomology

• differential K-theory

• differential elliptic cohomology

• differential cobordism cohomology

• ## Higher nonabelian differential cohomology

• Chern-Weil theory in Smooth∞Grpd

• ∞-Chern-Simons theory

• ## Fiber integration

• higher holonomy

• fiber integration in differential cohomology

• ## Application to gauge theory

• gauge theory

• gauge field

• quantum anomaly

• # Contents

## Idea

Twisted differential K-theory is the twisted differential cohomology version K-theory: the combination of differential K-theory and twisted K-theory.

Roughly this is an extension of twisted de Rham cohomology by twisted K-theory via the twisted Chern character map.

## References

Preliminary discussion included

• Alan Carey, Differential twisted K-theory and applications , ESI preprint (pdf)

and specifically the need for twisted differential K-theory for the description of type II string theory backgrounds with their RR-fields and B-fields on orientifolds was highlighted in

A definition and proof of its pertinent properties of twisted differential cohomology in general and of twisted differential K-theory in particular is due to

(in terms of smooth spectra such as discussed at differential cohomology diagram and tangent cohesive (∞,1)-topos).

Last revised on June 18, 2014 at 09:30:53. See the history of this page for a list of all contributions to it.