The equivariant simplicial de Rham complex and the classifying space of a semi-direct product group

TL;DR

This paper establishes an isomorphism between the cohomology of the equivariant simplicial de Rham complex and the cohomology of the classifying space for semi-direct product groups, advancing understanding of their topological properties.

Contribution

It introduces a novel connection between equivariant simplicial de Rham cohomology and classifying spaces for semi-direct product groups.

Findings

Cohomology groups are isomorphic.

Provides a new perspective on classifying spaces.

Enhances tools for studying semi-direct product groups.

Abstract

We show that the cohomology group of the equivariant simplicial de Rham complex is isomorphic to the cohomology group of the classifying space of a semi-direct product group.