# Equivariant de Rham Cohomology: Theory and Applications

## TL;DR

This survey explores the theory of equivariant de Rham cohomology for Lie group actions on manifolds, emphasizing formality and applications to cohomology and fixed points.

## Contribution

It provides a comprehensive overview of equivariant de Rham cohomology, highlighting the concept of equivariant formality and its applications.

## Key findings

- Equivariant formality simplifies the computation of cohomology.
- Applications include understanding fixed point sets and ordinary cohomology.
- The survey connects theory with practical applications in geometry.

## Abstract

This is a survey on the equivariant cohomology of Lie group actions on manifolds, from the point of view of de Rham theory. Emphasis is put on the notion of equivariant formality, as well as on applications to ordinary cohomology and to fixed points.