2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134722We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher dimensions. We examine its ramifications in systolic topology, and provide a sufficient condition for ensuring a lower bound of 3 for systolic category.22 pages; new section addedAlgebraic TopologyDifferential Geometry53C23; 55M30, 57N65text