On the equivariant cohomology of hyperpolar actions on symmetric spaces

TL;DR

This paper proves that the equivariant cohomology rings of hyperpolar actions on compact symmetric spaces are Cohen-Macaulay, extending previous results and deepening understanding of the algebraic structure of these actions.

Contribution

It establishes the Cohen-Macaulay property for equivariant cohomology of hyperpolar actions on symmetric spaces, generalizing earlier findings.

Findings

Equivariant cohomology rings are Cohen-Macaulay.

Generalization of previous results to broader class of actions.

Enhanced understanding of algebraic structures in symmetric spaces.

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.