A Chern-Weil Isomorphism for the Equivariant Brauer Group

TL;DR

This paper develops a Chern-Weil isomorphism connecting the equivariant Brauer group of R^n-actions on principal torus bundles to a dimensionally reduced Cech cohomology, revealing new structural insights.

Contribution

It introduces a novel Chern-Weil isomorphism for the equivariant Brauer group in the context of R^n-actions on torus bundles, linking it to reduced cohomology.

Findings

Establishes a Chern-Weil isomorphism for equivariant Brauer groups.

Connects the forgetful functor to a connecting homomorphism in cohomology.

Provides a new perspective on the structure of equivariant Brauer groups.

Abstract

In this paper we construct a Chern-Weil isomorphism for the equivariant Brauer group of R^n-actions on a principal torus bundle, where the target for this isomorphism is a "dimensionally reduced" Cech cohomology group. From this point of view, the usual forgetful functor takes the form of a connecting homomorphism in a long exact sequence in dimensionally reduced cohomology.