A Kunneth formula for Bredon cohomology of pullbacks and twisted K-theory of some 6-dimensional orbifolds

TL;DR

This paper develops a Kunneth formula for Bredon cohomology of pullback group actions and applies it to compute orbifold twisted K-theory for specific 6-dimensional orbifolds, illustrating both its utility and limitations.

Contribution

It introduces a new Kunneth formula for Bredon cohomology in the context of pullback group actions and demonstrates its application to orbifold twisted K-theory calculations.

Findings

Computed orbifold K-theory for certain 6-dimensional orbifolds.

Demonstrated the use of the Kunneth formula in practical calculations.

Identified limitations of the method in specific cases.

Abstract

In this paper we show a Kunneth formula for Bredon cohomology for actions of a pullback of groups. We show how this formula can be used to compute orbifold twisted K-theory for some discrete twistings. Using that result we compute orbifold K-theory for some 6-dimensional orbifolds introduced by Vafa and Witten. These examples also show the limitations of the method.