# nLab twisted equivariant K-theory

Contents

cohomology

### Theorems

#### Representation theory

representation theory

geometric representation theory

# Contents

## Idea

Twisted equivariant K-theory is the special case of twisted equivariant cohomology for the case that the cohomology theory is K-theory (often understood to be topological K-theory, by default), hence the joint generalization of twisted K-theory and equivariant K-theory.

This is often considered in the special case of twisted ad-equivariant K-theory.

## References

In a context of orbifold K-theory and for torsion class twists (“discrete torsion”):

With an eye towards twisted ad-equivariant K-theory:

In terms of bundle gerbes on differentiable stacks:

General definition in terms of equivariant sections of equivariant bundles of equivariant classifying spaces for equivariant K-theory:

Reviewed in:

Alternatively, in terms of Grothendieck groups of equivariant twisted vector bundles:

On the cohomology ring-structure:

The corresponding version of the Atiyah-Hirzebruch spectral sequence:

Relation to projective representations:

• José Manuel Gómez, Johana Ramírez, A Decomposition of twisted equivariant K-theory (arXiv:2001.02164)

Last revised on May 13, 2022 at 16:35:37. See the history of this page for a list of all contributions to it.