Small values of the Lusternik-Schnirelmann category for manifolds

Details Small values of the Lusternik-Schnirelmann category for manifolds Small values of the Lusternik-Schnirelmann category for manifolds

2008-05-11

arxiv.org/abs/0805.1527v1

Mathematics

Algebraic Topology

16 pages, to appear in Geometry and Topology

Scientific paper

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.

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