# nLab twisted differential K-theory

### Context

#### Differential cohomology

differential cohomology

# 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).

Revised on June 18, 2014 09:30:53 by David Corfield (31.185.244.23)