Bott conjecture on non-negatively curved manifolds

Let $M$ be a compact simply connected Riemannian manifold with non-negative sectional curvature. A topological space is rationally elliptic when its total rational homotopy and homology dimensions are finite.

Bott conjecture. The manifold $M$ is rationally elliptic.

The conjecture is a central question in Riemannian geometry and is sometimes called the Bott–Grove–Halperin conjecture. The source notes partial results under stronger assumptions, but does not state a general resolution.