The equivariant Brauer groups of commuting free and proper actions are isomorphic

TL;DR

This paper proves that for a space with commuting free and proper actions of two groups, the associated equivariant Brauer groups are naturally isomorphic, revealing a deep symmetry in their structure.

Contribution

It establishes a natural isomorphism between the equivariant Brauer groups under commuting free and proper group actions, extending understanding of their algebraic structure.

Findings

Brauer groups $ ext{Br}_H(G/X)$ and $ ext{Br}_G(X/H)$ are isomorphic

The isomorphism is natural and respects the group actions

Provides a new perspective on symmetry in equivariant algebraic topology

Abstract

If $X$ is a locally compact space which admits commuting free and proper actions of locally compact groups $G$ and $H$, then the Brauer groups $\Br_H(G/X)$ and $\Br_G(X/H)$ are naturally isomorphic.