# On the equivariant cohomology of $\mathbb{Z}_2\times\mathbb{Z}_k$-symmetric spaces

## TL;DR

This paper investigates the equivariant cohomology of $bZ_2 imes bZ_k$-symmetric spaces, providing evidence that their isotropy actions are equivariantly formal, which implies their formality in Rational Homotopy Theory.

## Contribution

It extends the understanding of equivariant cohomology for $bZ_2 imes bZ_k$-symmetric spaces and shows their isotropy actions are equivariantly formal.

## Key findings

- Isotropy actions are equivariantly formal for these spaces
- $bZ_2 imes bZ_k$-symmetric spaces are formal in Rational Homotopy Theory
- Provides evidence supporting conjectures on $bZ_2 imes bZ_k$-symmetric spaces

## Abstract

$\Gamma$-symmetric spaces are a vast generalization of symmetric spaces. Previous results make it conceivable that their isotropy action is equivariantly formal, and we provide evidence for this in case that $\Gamma = \mathbb{Z}_2\times\mathbb{Z}_k$. This in particular implies that $\mathbb{Z}_2\times\mathbb{Z}_k$-symmetric spaces are formal in the sense of Rational Homotopy Theory.