The classification conjecture for irreducible polar actions on compact nonnegatively curved manifolds

Let a compact Lie group act smoothly and isometrically on a simply connected compact manifold of nonnegative curvature. The action is irreducible when its associated reflection group has no invariant subspace, equivalently no totally geodesic invariant submanifold. The irreducible polar action conjecture. An irreducible polar action on a simply connected nonnegatively curved compact manifold is equivariantly diffeomorphic to a quotient of a polar action on a symmetric space. This conjecture proposes that irreducible polar actions in nonnegative curvature are modeled, up to equivariant diffeomorphism and quotient, by polar actions on symmetric spaces; the supplied text gives no resolution, so its general status remains open.