2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152165The survey is devoted to Toponogov's conjecture, that {\it if a complete simply connected Riemannian manifold with sectional curvature $\le 4$ and injectivity radius $\ge π/2$ has extremal diameter $π/2$, then it is isometric to CROSS}. In Section 1 the relations of problem with geodesic foliations of a round sphere are considered, but the proof of conjecture on this way is not complete. In Section 2 the proof based on recent results and methods for topology and volume of Blaschke manifolds is given.AMS-TeX v 2.1, 13 pagesDifferential Geometry53C12 (Primary) 53C20 (Secondary)text