We prove that manifolds of Lusternik–Schnirelmann category necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larrañaga and Gonzalez-Acuña by generalizing their result in dimension to all higher dimensions. We also obtain some general results on the relations between the fundamental group of a closed manifold , the dimension of and the Lusternik–Schnirelmann category of , and we relate the latter to the systolic category of .
"Small values of the Lusternik–Schnirelmann category for manifolds." Geom. Topol. 12 (3) 1711 - 1727, 2008. https://doi.org/10.2140/gt.2008.12.1711