2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217704We prove the Gromov conjecture on the macroscopic dimension of the universal covering of a closed spin manifold with a positive scalar curvature under the following assumptions on the fundamental group: 1. The Strong Novikov Conjecture holds for $π$. 2. The natural map $per:ko_n(Bπ)\to KO_n(Bπ)$ is injective.10 pagesGeometric TopologyAlgebraic Topology55M30, 53C23text