Abstract
We 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 also obtain some general results on the relations between the fundamental group of a closed manifold M , the dimension of M and the Lusternik–Schnirelmann category of M , and we relate the latter to the systolic category of M .
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