nLab
twisted equivariant K-theory

Contents

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

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:

The corresponding version of the Atiyah-Hirzebruch spectral sequence:

On equivariant principal bundles with structure group the projective unitary group, providing twists for twisted equivariant K-theory:

Relation to projective representations:

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

Last revised on June 18, 2021 at 12:46:50. See the history of this page for a list of all contributions to it.