Equivariant formality of isotropic torus actions

Abstract

Considering the potential equivariant formality of the left action of a connected Lie group $K$ on the homogeneous space $G/K$, we arrive through a sequence of reductions at the case $G$ is compact and simply-connected and $K$ is a torus. We then classify all pairs $(G,S)$ such that $G$ is compact connected Lie and the embedded circular subgroup $S$ acts equivariantly formally on $G/S$. In the process we provide a proof of the structure (known to Leray and Koszul) of the cohomology rings $H^{\ast }(G/S;\mathbb{Q})$.

Updated to match published version, modulo formatting and updated reference to one later-published result cited without proof here. Journal reference and DOI added

Cited by in corpus (4)

• Grassmannians and the equivariant cohomology of isotropy actions
• Equivariant formality of corank-one isotropy actions and products of rational spheres
• Equivariant de Rham Cohomology: Theory and Applications
• K-theory and formality