Equivariant principal bundles and their classifying spaces

TL;DR

This paper develops a theory for b3-equivariant principal G-bundles over proper b3-CW-complexes, constructing classifying spaces for certain topological groups, advancing understanding of equivariant bundle classification.

Contribution

It introduces a new construction of classifying spaces for b3-equivariant principal G-bundles with prescribed local representations, extending previous frameworks to broader classes of groups.

Findings

Constructed classifying spaces for b3-equivariant principal G-bundles.

Analyzed properties of these classifying spaces for locally compact, second countable groups.

Extended equivariant bundle theory to include groups with finite covering dimension and almost connected G.

Abstract

We consider \Gamma-equivariant principal G-bundles over proper \Gamma-CW-complexes with prescribed family of local representations. We construct and analyze their classifying spaces for locally compact, second countable topological groups with finite covering dimension \Gamma and G such that G is almost connected.