The equivariant cohomology ring of a cohomogeneity-one action

TL;DR

This paper calculates the rational Borel equivariant cohomology ring for a specific class of group actions with cohomogeneity one, providing explicit algebraic descriptions.

Contribution

It offers a novel computation of the equivariant cohomology ring for cohomogeneity-one actions of compact Lie groups, advancing understanding in equivariant topology.

Findings

Explicit description of the cohomology ring

Methodology for cohomogeneity-one actions

Applications to equivariant topology

Abstract

We compute the rational Borel equivariant cohomology ring of a cohomogeneity-one action of a compact Lie group.