The Cartan Model for Equivariant Cohomology

TL;DR

This paper introduces a new operator and Cartan model for equivariant cohomology, establishing connections with BRST and Weil models to advance the mathematical framework in this area.

Contribution

It presents a novel operator and Cartan model for equivariant cohomology, linking it with existing BRST and Weil models for the first time.

Findings

New operator $d_{C}$ defined on $W(rak{g}) ensor ext{Omega}^*(M)$

Constructed a new Cartan model for equivariant cohomology

Established relations between Cartan, BRST, and Weil models

Abstract

In this article, we will discuss a new operator $d_{C}$ on $W(\mathfrak{g})\otimes\Omega^{*}(M)$ and to construct a new Cartan model for equivariant cohomology. We use the new Cartan model to construct the corresponding BRST model and Weil model, and discuss the relations between them.