---
abstract: 'We show that the equivariant cohomology of any hyperpolar action of a compact and connected Lie group on a symmetric space of compact type is a Cohen-Macaulay ring. This generalizes some results previously obtained by the authors.'
address:
- |
    Department of Mathematics and Computer Science\
    Philipps-Universität Marburg\
    Germany
- |
    Institut für Geometrie und Topologie\
    Universität Stuttgart\
    Germany
- |
    Department of Mathematics and Statistics\
    University of Regina\
    Canada
author:
- Oliver Goertsches
- Sam Hagh Shenas Noshari
- 'Augustin-Liviu Mare'
title: On the equivariant cohomology of hyperpolar actions on symmetric spaces 
---

Introduction {#intro}
============

When investigating smooth group actions on manifolds, an insightful topological invariant one associates to it is its equivariant cohomology. (The coefficient ring throughout this paper is $\bQ$, unless otherwise specified.) This remains an effective tool even in cases when concrete descriptions are hard to obtain. Geometric features of the action are reflected by algebraic properties of its equivariant cohomology. Equivariant formality is an example of such a property, which is relevant due to its simple definition (see Sect. \[sec:general\]) and to the numerous situations when it is satisfied, such as Hamiltonian actions of compact Lie groups on compact symplectic manifolds (cf. 