Small values of the Lusternik-Schnirelmann category for manifolds

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 relate the latter to the systolic category of M.

16 pages, to appear in Geometry and Topology

References in corpus (2)

• On the Berstein-Svarc Theorem in dimension 2
• On the Lusternik-Schnirelmann category of spaces with 2-dimensional fundamental group