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 what seems to be the first published proof of the structure (known to Leray and Koszul) of the cohomology rings